How to rewrite $left[ begin{array}{c|c} I_{r}otimes (K e_1) \ vdots\ I_{r}otimes (K e_n) end{array} right]$?











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I have the following matrix: $left[
begin{array}{c|c}
I_{r}otimes (K e_1) \
vdots\
I_{r}otimes (K e_n)
end{array}
right]$



$e_i$ is the i-th column of the identity matrix with the same dimensions as $K_{ntimes n}$. $otimes$ is the kronecker product.



I want to rewrite it in a way that $K$, or $vec(K)$, etc., is outside.






matrices tensor-products matrix-calculus







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  • $K$ is the field you are working over?
    – Vincent
    Nov 9 at 12:36






  • 1




    @Vincent K is another matrix
    – An old man in the sea.
    Nov 9 at 12:57















up vote
0
down vote

favorite












I have the following matrix: $left[
begin{array}{c|c}
I_{r}otimes (K e_1) \
vdots\
I_{r}otimes (K e_n)
end{array}
right]$



$e_i$ is the i-th column of the identity matrix with the same dimensions as $K_{ntimes n}$. $otimes$ is the kronecker product.



I want to rewrite it in a way that $K$, or $vec(K)$, etc., is outside.






matrices tensor-products matrix-calculus







share|cite|improve this question
























  • $K$ is the field you are working over?
    – Vincent
    Nov 9 at 12:36






  • 1




    @Vincent K is another matrix
    – An old man in the sea.
    Nov 9 at 12:57













up vote
0
down vote

favorite









up vote
0
down vote

favorite











I have the following matrix: $left[
begin{array}{c|c}
I_{r}otimes (K e_1) \
vdots\
I_{r}otimes (K e_n)
end{array}
right]$



$e_i$ is the i-th column of the identity matrix with the same dimensions as $K_{ntimes n}$. $otimes$ is the kronecker product.



I want to rewrite it in a way that $K$, or $vec(K)$, etc., is outside.






matrices tensor-products matrix-calculus







share|cite|improve this question















I have the following matrix: $left[
begin{array}{c|c}
I_{r}otimes (K e_1) \
vdots\
I_{r}otimes (K e_n)
end{array}
right]$



$e_i$ is the i-th column of the identity matrix with the same dimensions as $K_{ntimes n}$. $otimes$ is the kronecker product.



I want to rewrite it in a way that $K$, or $vec(K)$, etc., is outside.






matrices tensor-products matrix-calculus




matrices tensor-products matrix-calculus






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited 21 hours ago

























asked Nov 9 at 11:56









An old man in the sea.

1,59411031




1,59411031












  • $K$ is the field you are working over?
    – Vincent
    Nov 9 at 12:36






  • 1




    @Vincent K is another matrix
    – An old man in the sea.
    Nov 9 at 12:57


















  • $K$ is the field you are working over?
    – Vincent
    Nov 9 at 12:36






  • 1




    @Vincent K is another matrix
    – An old man in the sea.
    Nov 9 at 12:57
















$K$ is the field you are working over?
– Vincent
Nov 9 at 12:36




$K$ is the field you are working over?
– Vincent
Nov 9 at 12:36




1




1




@Vincent K is another matrix
– An old man in the sea.
Nov 9 at 12:57




@Vincent K is another matrix
– An old man in the sea.
Nov 9 at 12:57










1 Answer
1






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Here's my try.



$(I_notimes I_rotimes K))left[
begin{array}{c|c}
I_{r}otimes e_1 \
vdots\
I_{r}otimes e_n
end{array}
right]$






share|cite|improve this answer





















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    1 Answer
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    up vote
    0
    down vote













    Here's my try.



    $(I_notimes I_rotimes K))left[
    begin{array}{c|c}
    I_{r}otimes e_1 \
    vdots\
    I_{r}otimes e_n
    end{array}
    right]$






    share|cite|improve this answer

























      up vote
      0
      down vote













      Here's my try.



      $(I_notimes I_rotimes K))left[
      begin{array}{c|c}
      I_{r}otimes e_1 \
      vdots\
      I_{r}otimes e_n
      end{array}
      right]$






      share|cite|improve this answer























        up vote
        0
        down vote










        up vote
        0
        down vote









        Here's my try.



        $(I_notimes I_rotimes K))left[
        begin{array}{c|c}
        I_{r}otimes e_1 \
        vdots\
        I_{r}otimes e_n
        end{array}
        right]$






        share|cite|improve this answer












        Here's my try.



        $(I_notimes I_rotimes K))left[
        begin{array}{c|c}
        I_{r}otimes e_1 \
        vdots\
        I_{r}otimes e_n
        end{array}
        right]$







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered Nov 9 at 12:59









        An old man in the sea.

        1,59411031




        1,59411031






























             

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