Matrix rows notation












7












$begingroup$


I'm working with a set of $M$ vectors $ {mathbf{w}_i in mathbb{R}^N, , i = 1, ldots, M }$. Since single vectors are usually considered as column vectors, I'm defining a matrix



$$
mathbf{W} = [mathbf{w}_1, ldots, mathbf{w}_M] in mathbb{R}^{N times M}
$$



by placing the vectors as matrix columns.



However, for some descriptions, I need to refer to the matrix rows.



Is there an elegant notation to refer to this matrix rows (preferably with less notation overhead)?






matrices notation







share|cite|improve this question









$endgroup$












  • $begingroup$
    What about $mathbf{W}_{ibullet}$ for the $i$th row?
    $endgroup$
    – Raskolnikov
    May 7 '13 at 6:23








  • 1




    $begingroup$
    Since I'm writing vectors in lower case I would write matrix rows as $mathbf{w}_{j*}$ for $j = 1, ldots, N$. However, I'm not sure if this dot or star symbol is a valid math notation.
    $endgroup$
    – Robinaut
    May 7 '13 at 7:06








  • 1




    $begingroup$
    It's very common. But even if it wasn't, you can always invent your own notation, as long as you define it so that readers know.
    $endgroup$
    – Raskolnikov
    May 7 '13 at 7:15
















7












$begingroup$


I'm working with a set of $M$ vectors $ {mathbf{w}_i in mathbb{R}^N, , i = 1, ldots, M }$. Since single vectors are usually considered as column vectors, I'm defining a matrix



$$
mathbf{W} = [mathbf{w}_1, ldots, mathbf{w}_M] in mathbb{R}^{N times M}
$$



by placing the vectors as matrix columns.



However, for some descriptions, I need to refer to the matrix rows.



Is there an elegant notation to refer to this matrix rows (preferably with less notation overhead)?






matrices notation







share|cite|improve this question









$endgroup$












  • $begingroup$
    What about $mathbf{W}_{ibullet}$ for the $i$th row?
    $endgroup$
    – Raskolnikov
    May 7 '13 at 6:23








  • 1




    $begingroup$
    Since I'm writing vectors in lower case I would write matrix rows as $mathbf{w}_{j*}$ for $j = 1, ldots, N$. However, I'm not sure if this dot or star symbol is a valid math notation.
    $endgroup$
    – Robinaut
    May 7 '13 at 7:06








  • 1




    $begingroup$
    It's very common. But even if it wasn't, you can always invent your own notation, as long as you define it so that readers know.
    $endgroup$
    – Raskolnikov
    May 7 '13 at 7:15














7












7








7


2



$begingroup$


I'm working with a set of $M$ vectors $ {mathbf{w}_i in mathbb{R}^N, , i = 1, ldots, M }$. Since single vectors are usually considered as column vectors, I'm defining a matrix



$$
mathbf{W} = [mathbf{w}_1, ldots, mathbf{w}_M] in mathbb{R}^{N times M}
$$



by placing the vectors as matrix columns.



However, for some descriptions, I need to refer to the matrix rows.



Is there an elegant notation to refer to this matrix rows (preferably with less notation overhead)?






matrices notation







share|cite|improve this question









$endgroup$




I'm working with a set of $M$ vectors $ {mathbf{w}_i in mathbb{R}^N, , i = 1, ldots, M }$. Since single vectors are usually considered as column vectors, I'm defining a matrix



$$
mathbf{W} = [mathbf{w}_1, ldots, mathbf{w}_M] in mathbb{R}^{N times M}
$$



by placing the vectors as matrix columns.



However, for some descriptions, I need to refer to the matrix rows.



Is there an elegant notation to refer to this matrix rows (preferably with less notation overhead)?






matrices notation




matrices notation






share|cite|improve this question













share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked May 7 '13 at 6:20









RobinautRobinaut

17016




17016












  • $begingroup$
    What about $mathbf{W}_{ibullet}$ for the $i$th row?
    $endgroup$
    – Raskolnikov
    May 7 '13 at 6:23








  • 1




    $begingroup$
    Since I'm writing vectors in lower case I would write matrix rows as $mathbf{w}_{j*}$ for $j = 1, ldots, N$. However, I'm not sure if this dot or star symbol is a valid math notation.
    $endgroup$
    – Robinaut
    May 7 '13 at 7:06








  • 1




    $begingroup$
    It's very common. But even if it wasn't, you can always invent your own notation, as long as you define it so that readers know.
    $endgroup$
    – Raskolnikov
    May 7 '13 at 7:15


















  • $begingroup$
    What about $mathbf{W}_{ibullet}$ for the $i$th row?
    $endgroup$
    – Raskolnikov
    May 7 '13 at 6:23








  • 1




    $begingroup$
    Since I'm writing vectors in lower case I would write matrix rows as $mathbf{w}_{j*}$ for $j = 1, ldots, N$. However, I'm not sure if this dot or star symbol is a valid math notation.
    $endgroup$
    – Robinaut
    May 7 '13 at 7:06








  • 1




    $begingroup$
    It's very common. But even if it wasn't, you can always invent your own notation, as long as you define it so that readers know.
    $endgroup$
    – Raskolnikov
    May 7 '13 at 7:15
















$begingroup$
What about $mathbf{W}_{ibullet}$ for the $i$th row?
$endgroup$
– Raskolnikov
May 7 '13 at 6:23






$begingroup$
What about $mathbf{W}_{ibullet}$ for the $i$th row?
$endgroup$
– Raskolnikov
May 7 '13 at 6:23






1




1




$begingroup$
Since I'm writing vectors in lower case I would write matrix rows as $mathbf{w}_{j*}$ for $j = 1, ldots, N$. However, I'm not sure if this dot or star symbol is a valid math notation.
$endgroup$
– Robinaut
May 7 '13 at 7:06






$begingroup$
Since I'm writing vectors in lower case I would write matrix rows as $mathbf{w}_{j*}$ for $j = 1, ldots, N$. However, I'm not sure if this dot or star symbol is a valid math notation.
$endgroup$
– Robinaut
May 7 '13 at 7:06






1




1




$begingroup$
It's very common. But even if it wasn't, you can always invent your own notation, as long as you define it so that readers know.
$endgroup$
– Raskolnikov
May 7 '13 at 7:15




$begingroup$
It's very common. But even if it wasn't, you can always invent your own notation, as long as you define it so that readers know.
$endgroup$
– Raskolnikov
May 7 '13 at 7:15










3 Answers
3






active

oldest

votes


















4












$begingroup$

You can represent the rows of $mathbf W$ by the $M$-(column-)vectors $mathbf w'_i :=mathrm{col}_imathbf W^mathsf T;(i=1,dots,N).$ There is no standard notation for this; I chose the prime notation for convenience. You would also need to state your chosen notation explicitly.






share|cite|improve this answer









$endgroup$





















    2












    $begingroup$

    Since $W_{nm}$ is unambiguous for the $n$th row, $m$th col entry of $W$, I quite like the following notation:



    begin{align}
    text{For rows:}& quad W_{n*} = W_{n,*} \
    text{For cols:}& quad W_{*m} = W_{*,m} \
    end{align}



    From a programming perspective, this is similar to how in R we use W[n,] and W[,m] and in Numpy we use W[n,:] and W[m,:].






    share|cite|improve this answer









    $endgroup$





















      -1












      $begingroup$

      If you write
      $$mathbf{W} = [mathbf{w}_1, ldots, mathbf{w}_M]^t in mathbb{R}^{M times N}$$
      then the rows of $mathbf W$ are $mathbf{w}_1^t, ldots, mathbf{w}_M^t$.






      share|cite|improve this answer









      $endgroup$









      • 2




        $begingroup$
        Well, yes, but that's not how $mathbf{W}$ was written (nor is it even necessarily of the correct dimension), so how does this help?
        $endgroup$
        – Cameron Buie
        May 7 '13 at 6:41










      • $begingroup$
        It's additional notation. Just use a different letter and set it equal to the original. Not that hard.
        $endgroup$
        – Jim
        May 7 '13 at 15:49











      Your Answer





      StackExchange.ifUsing("editor", function () {
      return StackExchange.using("mathjaxEditing", function () {
      StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
      StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
      });
      });
      }, "mathjax-editing");

      StackExchange.ready(function() {
      var channelOptions = {
      tags: "".split(" "),
      id: "69"
      };
      initTagRenderer("".split(" "), "".split(" "), channelOptions);

      StackExchange.using("externalEditor", function() {
      // Have to fire editor after snippets, if snippets enabled
      if (StackExchange.settings.snippets.snippetsEnabled) {
      StackExchange.using("snippets", function() {
      createEditor();
      });
      }
      else {
      createEditor();
      }
      });

      function createEditor() {
      StackExchange.prepareEditor({
      heartbeatType: 'answer',
      autoActivateHeartbeat: false,
      convertImagesToLinks: true,
      noModals: true,
      showLowRepImageUploadWarning: true,
      reputationToPostImages: 10,
      bindNavPrevention: true,
      postfix: "",
      imageUploader: {
      brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
      contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
      allowUrls: true
      },
      noCode: true, onDemand: true,
      discardSelector: ".discard-answer"
      ,immediatelyShowMarkdownHelp:true
      });


      }
      });














      draft saved

      draft discarded


















      StackExchange.ready(
      function () {
      StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f384153%2fmatrix-rows-notation%23new-answer', 'question_page');
      }
      );

      Post as a guest















      Required, but never shown

























      3 Answers
      3






      active

      oldest

      votes








      3 Answers
      3






      active

      oldest

      votes









      active

      oldest

      votes






      active

      oldest

      votes









      4












      $begingroup$

      You can represent the rows of $mathbf W$ by the $M$-(column-)vectors $mathbf w'_i :=mathrm{col}_imathbf W^mathsf T;(i=1,dots,N).$ There is no standard notation for this; I chose the prime notation for convenience. You would also need to state your chosen notation explicitly.






      share|cite|improve this answer









      $endgroup$


















        4












        $begingroup$

        You can represent the rows of $mathbf W$ by the $M$-(column-)vectors $mathbf w'_i :=mathrm{col}_imathbf W^mathsf T;(i=1,dots,N).$ There is no standard notation for this; I chose the prime notation for convenience. You would also need to state your chosen notation explicitly.






        share|cite|improve this answer









        $endgroup$
















          4












          4








          4





          $begingroup$

          You can represent the rows of $mathbf W$ by the $M$-(column-)vectors $mathbf w'_i :=mathrm{col}_imathbf W^mathsf T;(i=1,dots,N).$ There is no standard notation for this; I chose the prime notation for convenience. You would also need to state your chosen notation explicitly.






          share|cite|improve this answer









          $endgroup$



          You can represent the rows of $mathbf W$ by the $M$-(column-)vectors $mathbf w'_i :=mathrm{col}_imathbf W^mathsf T;(i=1,dots,N).$ There is no standard notation for this; I chose the prime notation for convenience. You would also need to state your chosen notation explicitly.







          share|cite|improve this answer












          share|cite|improve this answer



          share|cite|improve this answer










          answered May 7 '13 at 8:24









          John BentinJohn Bentin

          11.3k22554




          11.3k22554























              2












              $begingroup$

              Since $W_{nm}$ is unambiguous for the $n$th row, $m$th col entry of $W$, I quite like the following notation:



              begin{align}
              text{For rows:}& quad W_{n*} = W_{n,*} \
              text{For cols:}& quad W_{*m} = W_{*,m} \
              end{align}



              From a programming perspective, this is similar to how in R we use W[n,] and W[,m] and in Numpy we use W[n,:] and W[m,:].






              share|cite|improve this answer









              $endgroup$


















                2












                $begingroup$

                Since $W_{nm}$ is unambiguous for the $n$th row, $m$th col entry of $W$, I quite like the following notation:



                begin{align}
                text{For rows:}& quad W_{n*} = W_{n,*} \
                text{For cols:}& quad W_{*m} = W_{*,m} \
                end{align}



                From a programming perspective, this is similar to how in R we use W[n,] and W[,m] and in Numpy we use W[n,:] and W[m,:].






                share|cite|improve this answer









                $endgroup$
















                  2












                  2








                  2





                  $begingroup$

                  Since $W_{nm}$ is unambiguous for the $n$th row, $m$th col entry of $W$, I quite like the following notation:



                  begin{align}
                  text{For rows:}& quad W_{n*} = W_{n,*} \
                  text{For cols:}& quad W_{*m} = W_{*,m} \
                  end{align}



                  From a programming perspective, this is similar to how in R we use W[n,] and W[,m] and in Numpy we use W[n,:] and W[m,:].






                  share|cite|improve this answer









                  $endgroup$



                  Since $W_{nm}$ is unambiguous for the $n$th row, $m$th col entry of $W$, I quite like the following notation:



                  begin{align}
                  text{For rows:}& quad W_{n*} = W_{n,*} \
                  text{For cols:}& quad W_{*m} = W_{*,m} \
                  end{align}



                  From a programming perspective, this is similar to how in R we use W[n,] and W[,m] and in Numpy we use W[n,:] and W[m,:].







                  share|cite|improve this answer












                  share|cite|improve this answer



                  share|cite|improve this answer










                  answered Apr 17 '18 at 18:12









                  qwrqwr

                  6,68342755




                  6,68342755























                      -1












                      $begingroup$

                      If you write
                      $$mathbf{W} = [mathbf{w}_1, ldots, mathbf{w}_M]^t in mathbb{R}^{M times N}$$
                      then the rows of $mathbf W$ are $mathbf{w}_1^t, ldots, mathbf{w}_M^t$.






                      share|cite|improve this answer









                      $endgroup$









                      • 2




                        $begingroup$
                        Well, yes, but that's not how $mathbf{W}$ was written (nor is it even necessarily of the correct dimension), so how does this help?
                        $endgroup$
                        – Cameron Buie
                        May 7 '13 at 6:41










                      • $begingroup$
                        It's additional notation. Just use a different letter and set it equal to the original. Not that hard.
                        $endgroup$
                        – Jim
                        May 7 '13 at 15:49
















                      -1












                      $begingroup$

                      If you write
                      $$mathbf{W} = [mathbf{w}_1, ldots, mathbf{w}_M]^t in mathbb{R}^{M times N}$$
                      then the rows of $mathbf W$ are $mathbf{w}_1^t, ldots, mathbf{w}_M^t$.






                      share|cite|improve this answer









                      $endgroup$









                      • 2




                        $begingroup$
                        Well, yes, but that's not how $mathbf{W}$ was written (nor is it even necessarily of the correct dimension), so how does this help?
                        $endgroup$
                        – Cameron Buie
                        May 7 '13 at 6:41










                      • $begingroup$
                        It's additional notation. Just use a different letter and set it equal to the original. Not that hard.
                        $endgroup$
                        – Jim
                        May 7 '13 at 15:49














                      -1












                      -1








                      -1





                      $begingroup$

                      If you write
                      $$mathbf{W} = [mathbf{w}_1, ldots, mathbf{w}_M]^t in mathbb{R}^{M times N}$$
                      then the rows of $mathbf W$ are $mathbf{w}_1^t, ldots, mathbf{w}_M^t$.






                      share|cite|improve this answer









                      $endgroup$



                      If you write
                      $$mathbf{W} = [mathbf{w}_1, ldots, mathbf{w}_M]^t in mathbb{R}^{M times N}$$
                      then the rows of $mathbf W$ are $mathbf{w}_1^t, ldots, mathbf{w}_M^t$.







                      share|cite|improve this answer












                      share|cite|improve this answer



                      share|cite|improve this answer










                      answered May 7 '13 at 6:31









                      JimJim

                      24.4k23370




                      24.4k23370








                      • 2




                        $begingroup$
                        Well, yes, but that's not how $mathbf{W}$ was written (nor is it even necessarily of the correct dimension), so how does this help?
                        $endgroup$
                        – Cameron Buie
                        May 7 '13 at 6:41










                      • $begingroup$
                        It's additional notation. Just use a different letter and set it equal to the original. Not that hard.
                        $endgroup$
                        – Jim
                        May 7 '13 at 15:49














                      • 2




                        $begingroup$
                        Well, yes, but that's not how $mathbf{W}$ was written (nor is it even necessarily of the correct dimension), so how does this help?
                        $endgroup$
                        – Cameron Buie
                        May 7 '13 at 6:41










                      • $begingroup$
                        It's additional notation. Just use a different letter and set it equal to the original. Not that hard.
                        $endgroup$
                        – Jim
                        May 7 '13 at 15:49








                      2




                      2




                      $begingroup$
                      Well, yes, but that's not how $mathbf{W}$ was written (nor is it even necessarily of the correct dimension), so how does this help?
                      $endgroup$
                      – Cameron Buie
                      May 7 '13 at 6:41




                      $begingroup$
                      Well, yes, but that's not how $mathbf{W}$ was written (nor is it even necessarily of the correct dimension), so how does this help?
                      $endgroup$
                      – Cameron Buie
                      May 7 '13 at 6:41












                      $begingroup$
                      It's additional notation. Just use a different letter and set it equal to the original. Not that hard.
                      $endgroup$
                      – Jim
                      May 7 '13 at 15:49




                      $begingroup$
                      It's additional notation. Just use a different letter and set it equal to the original. Not that hard.
                      $endgroup$
                      – Jim
                      May 7 '13 at 15:49


















                      draft saved

                      draft discarded




















































                      Thanks for contributing an answer to Mathematics Stack Exchange!


                      • Please be sure to answer the question. Provide details and share your research!

                      But avoid …



                      • Asking for help, clarification, or responding to other answers.

                      • Making statements based on opinion; back them up with references or personal experience.


                      Use MathJax to format equations. MathJax reference.


                      To learn more, see our tips on writing great answers.




                      draft saved


                      draft discarded














                      StackExchange.ready(
                      function () {
                      StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f384153%2fmatrix-rows-notation%23new-answer', 'question_page');
                      }
                      );

                      Post as a guest















                      Required, but never shown





















































                      Required, but never shown














                      Required, but never shown












                      Required, but never shown







                      Required, but never shown

































                      Required, but never shown














                      Required, but never shown












                      Required, but never shown







                      Required, but never shown







                      Popular posts from this blog

                      MongoDB - Not Authorized To Execute Command

                      Image
                      .everyoneloves__top-leaderboard:empty,.everyoneloves__mid-leaderboard:empty,.everyoneloves__bot-mid-leaderboard:empty{ height:90px;width:728px;box-sizing:border-box; } 0 I have successfully enabled authorization on MongoDB and I have created an account on the admin database and then I created an account for my database called test. The following connection string to connect to my test database works successfully: mongo --host 192.168.17.52 --port 27017 -u user1 -p password --authenticationDatabase test Only problem I have now is, I cannot execute commands such as: show dbs. I get the following error when I try to do so: "errmsg" : "not authorized on admin to execute command { listDatabases: 1.0, lsid: { id: UUID("a1d5bc0d-bc58-485e-b232-270758a89455") }, $db: "admin...
                      Read more

                      in spring boot 2.1 many test slices are not allowed anymore due to multiple @BootstrapWith

                      Image
                      1 I tried to upgrade a yummy sandwich made of two test slices (@JsonTest and @JdbcTest in my case, crunchy test code in between) adding spring boot 2.1 flavour to it. But it seems it was not much of a success. I cannot annotate my tests with many @...Test since they are now each bringing their own XxxTestContextBootstrapper. It used to work when they all used same SpringBootTestContextBootstrapper. @RunWith(SpringRunner.class) @JdbcTest @JsonTest public class Test { @Test public void test() { System.out.printn("Hello, World !"); } } The error I get from BootstrapUtils is illegalStateException : Configuration error: found multiple declarations of @BootstrapWith for test class I understand I might be doing something wrong here but is there an easy way I could load both Json and Jdbc contex...
                      Read more

                      Npm cannot find a required file even through it is in the searched directory

                      Image
                      up vote 0 down vote favorite I got that error: users-Air:pdfuploader user$ npm run start client@0.1.0 start /Users/user/Documents/pdfuploader react-scripts start Could not find a required file. Name: index.html Searched in: /Users/user/Documents/pdfuploader/public npm ERR! code ELIFECYCLE npm ERR! errno 1 npm ERR! client@0.1.0 start: `react-scripts start` npm ERR! Exit status 1 npm ERR! npm ERR! Failed at the client@0.1.0 start script. npm ERR! This is probably not a problem with npm. There is likely additional logging output above. npm ERR! A complete log of this run can be found in: npm ERR! /Users/user/.npm/_logs/2018-11-19T10_19_14_555Z-debug.log users-Air:pdfuploader user$ And the file is in /Users/user/Documents/pdfuploader/public as you can see in my github repository: https://github.c...
                      Read more