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basis of a subspace that generates all of $Bbb R^3$
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I have a set of all $3times3$ matrices $B$ that have rank $0, 1$ or $2$ - what is the basis of a subspace that this set generates?
I came to the conclusion that this subspace consists of lines, planes and the null vector and it generates the whole space of $Bbb R^3$, but I don't know what is the basis of this subspace - is it just the set of all the $B$'s?
linear-algebra matrices matrix-rank
edited 22 hours ago
Tianlalu
2,559632
asked 22 hours ago
agromek
1
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agromek is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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add a comment |
up vote
0
down vote
favorite
I have a set of all $3times3$ matrices $B$ that have rank $0, 1$ or $2$ - what is the basis of a subspace that this set generates?
I came to the conclusion that this subspace consists of lines, planes and the null vector and it generates the whole space of $Bbb R^3$, but I don't know what is the basis of this subspace - is it just the set of all the $B$'s?
linear-algebra matrices matrix-rank
edited 22 hours ago
Tianlalu
2,559632
asked 22 hours ago
agromek
1
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agromek is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
– José Carlos Santos
22 hours ago
add a comment |
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favorite
up vote
0
down vote
favorite
I have a set of all $3times3$ matrices $B$ that have rank $0, 1$ or $2$ - what is the basis of a subspace that this set generates?
I came to the conclusion that this subspace consists of lines, planes and the null vector and it generates the whole space of $Bbb R^3$, but I don't know what is the basis of this subspace - is it just the set of all the $B$'s?
linear-algebra matrices matrix-rank
edited 22 hours ago
Tianlalu
2,559632
asked 22 hours ago
agromek
1
New contributor
agromek is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
I have a set of all $3times3$ matrices $B$ that have rank $0, 1$ or $2$ - what is the basis of a subspace that this set generates?
I came to the conclusion that this subspace consists of lines, planes and the null vector and it generates the whole space of $Bbb R^3$, but I don't know what is the basis of this subspace - is it just the set of all the $B$'s?
linear-algebra matrices matrix-rank
linear-algebra matrices matrix-rank
edited 22 hours ago
Tianlalu
2,559632
asked 22 hours ago
agromek
1
New contributor
agromek is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 22 hours ago
Tianlalu
2,559632
asked 22 hours ago
agromek
1
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agromek is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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edited 22 hours ago
Tianlalu
2,559632
edited 22 hours ago
Tianlalu
2,559632
edited 22 hours ago
Tianlalu
2,559632
2,559632
asked 22 hours ago
agromek
1
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agromek is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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asked 22 hours ago
agromek
1
asked 22 hours ago
agromek
1
1
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agromek is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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New contributor
agromek is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
agromek is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
– José Carlos Santos
22 hours ago
add a comment |
Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
– José Carlos Santos
22 hours ago
Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
– José Carlos Santos
22 hours ago
Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
– José Carlos Santos
22 hours ago
add a comment |
2 Answers
2
active
oldest
votes
up vote
0
down vote
It's unclear which space you're talking about---subspace of what? If you are viewing $3times3$ matrices as elements of $V=mathbb R^{3,3}$ i.e. $3times3$ matrices under addition, then the answer is all of $V$.
answered 22 hours ago
Richard Martin
1,2588
the set of B matrices is the subspace of R^3
– agromek
22 hours ago
No, I don't think so.
– Richard Martin
22 hours ago
the whole task was that I have two 3x3 matrices: A and C - A has rank 2 and C can be any 3x3 matrix and the question is: what is the basis of a subspace of the space of all 3x3 matrices that is generated by the set of 3x3 matrices B that satisfy the equation A*C=B (I'm trying to translate it into english as exact as I can)
– agromek
22 hours ago
maybe I'm interpreting the phrase "the space of all 3x3 matrices" wrongly, I thought it is just R^3 but maybe it's something else?
– agromek
22 hours ago
The space of all 3x3 matrices acts on $mathbb R^3$ but it is not of itself $mathbb R^3$.
– Richard Martin
22 hours ago
|
show 2 more comments
up vote
0
down vote
The vector space of all $3 x 3$ matrices is not $R^3$. You can verify that the space has dimension $9$ because you will need $9$ vectors for a basis. Probably the most likely ones would be $begin{bmatrix}1 & 0 & 0\0 & 0 & 0\0 & 0 & 0end{bmatrix}$, $begin{bmatrix}0 & 1 & 0\0 & 0 & 0\0 & 0 & 0end{bmatrix}$ ... $begin{bmatrix}0 & 0 & 1\0 & 0 & 0\0 & 0 & 0end{bmatrix}$,$begin{bmatrix}0 & 0 & 0\1 & 0 & 0\0 & 0 & 0end{bmatrix}$, $begin{bmatrix}0 & 0 & 0\0 & 1 & 0\0 & 0 & 0end{bmatrix}$, $begin{bmatrix}0 & 0 & 0\0 & 0 & 1\0 & 0 & 0end{bmatrix}$,$begin{bmatrix}0 & 0 & 0\0 & 0 & 0\1 & 0 & 0end{bmatrix}$, $begin{bmatrix}0 & 0 & 0\0 & 0 & 0\0 & 1 & 0end{bmatrix}$, $begin{bmatrix}0 & 0 & 0\0 & 0 & 0\0 & 0 & 1end{bmatrix}$
Now considering that your subspace only contains matrices with rank $leq2$ the basis for that space will contain only $6$ of these $9$.
answered 20 hours ago
Chai
1012
New contributor
Chai is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
SInce all those matrices have rank $le2$, they all belong to the given set.
– egreg
20 hours ago
Is that true? Taking linear combinations of all $9$ will yield all possible matrices, including rank $3$ ones. If we leave out the ones that have 1's in the last column ofr instance, all combinations will have rank $leq2$ , or am I missing something?
– Chai
20 hours ago
Well, every matrix belongs to the span of the rank $1$ matrices.
– egreg
20 hours ago
I'm not quite sure what you mean by that. As I understand it, OP is looking for a basis of the subspace of $3x3$ matrices that do not include the ones with rank$3$. I believe you could find a basis in this manner. But if I am wrong I'd like to learn as well !
– Chai
20 hours ago
I don't really understand why the vector space of all 3x3 matrices has dimension 9? can someone please explain?
– agromek
16 hours ago
|
show 3 more comments
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
It's unclear which space you're talking about---subspace of what? If you are viewing $3times3$ matrices as elements of $V=mathbb R^{3,3}$ i.e. $3times3$ matrices under addition, then the answer is all of $V$.
answered 22 hours ago
Richard Martin
1,2588
the set of B matrices is the subspace of R^3
– agromek
22 hours ago
No, I don't think so.
– Richard Martin
22 hours ago
the whole task was that I have two 3x3 matrices: A and C - A has rank 2 and C can be any 3x3 matrix and the question is: what is the basis of a subspace of the space of all 3x3 matrices that is generated by the set of 3x3 matrices B that satisfy the equation A*C=B (I'm trying to translate it into english as exact as I can)
– agromek
22 hours ago
maybe I'm interpreting the phrase "the space of all 3x3 matrices" wrongly, I thought it is just R^3 but maybe it's something else?
– agromek
22 hours ago
The space of all 3x3 matrices acts on $mathbb R^3$ but it is not of itself $mathbb R^3$.
– Richard Martin
22 hours ago
|
show 2 more comments
up vote
0
down vote
It's unclear which space you're talking about---subspace of what? If you are viewing $3times3$ matrices as elements of $V=mathbb R^{3,3}$ i.e. $3times3$ matrices under addition, then the answer is all of $V$.
answered 22 hours ago
Richard Martin
1,2588
the set of B matrices is the subspace of R^3
– agromek
22 hours ago
No, I don't think so.
– Richard Martin
22 hours ago
the whole task was that I have two 3x3 matrices: A and C - A has rank 2 and C can be any 3x3 matrix and the question is: what is the basis of a subspace of the space of all 3x3 matrices that is generated by the set of 3x3 matrices B that satisfy the equation A*C=B (I'm trying to translate it into english as exact as I can)
– agromek
22 hours ago
maybe I'm interpreting the phrase "the space of all 3x3 matrices" wrongly, I thought it is just R^3 but maybe it's something else?
– agromek
22 hours ago
The space of all 3x3 matrices acts on $mathbb R^3$ but it is not of itself $mathbb R^3$.
– Richard Martin
22 hours ago
|
show 2 more comments
up vote
0
down vote
up vote
0
down vote
It's unclear which space you're talking about---subspace of what? If you are viewing $3times3$ matrices as elements of $V=mathbb R^{3,3}$ i.e. $3times3$ matrices under addition, then the answer is all of $V$.
answered 22 hours ago
Richard Martin
1,2588
It's unclear which space you're talking about---subspace of what? If you are viewing $3times3$ matrices as elements of $V=mathbb R^{3,3}$ i.e. $3times3$ matrices under addition, then the answer is all of $V$.
answered 22 hours ago
Richard Martin
1,2588
answered 22 hours ago
Richard Martin
1,2588
answered 22 hours ago
Richard Martin
1,2588
answered 22 hours ago
Richard Martin
1,2588
1,2588
the set of B matrices is the subspace of R^3
– agromek
22 hours ago
No, I don't think so.
– Richard Martin
22 hours ago
the whole task was that I have two 3x3 matrices: A and C - A has rank 2 and C can be any 3x3 matrix and the question is: what is the basis of a subspace of the space of all 3x3 matrices that is generated by the set of 3x3 matrices B that satisfy the equation A*C=B (I'm trying to translate it into english as exact as I can)
– agromek
22 hours ago
maybe I'm interpreting the phrase "the space of all 3x3 matrices" wrongly, I thought it is just R^3 but maybe it's something else?
– agromek
22 hours ago
The space of all 3x3 matrices acts on $mathbb R^3$ but it is not of itself $mathbb R^3$.
– Richard Martin
22 hours ago
|
show 2 more comments
the set of B matrices is the subspace of R^3
– agromek
22 hours ago
No, I don't think so.
– Richard Martin
22 hours ago
the whole task was that I have two 3x3 matrices: A and C - A has rank 2 and C can be any 3x3 matrix and the question is: what is the basis of a subspace of the space of all 3x3 matrices that is generated by the set of 3x3 matrices B that satisfy the equation A*C=B (I'm trying to translate it into english as exact as I can)
– agromek
22 hours ago
maybe I'm interpreting the phrase "the space of all 3x3 matrices" wrongly, I thought it is just R^3 but maybe it's something else?
– agromek
22 hours ago
The space of all 3x3 matrices acts on $mathbb R^3$ but it is not of itself $mathbb R^3$.
– Richard Martin
22 hours ago
the set of B matrices is the subspace of R^3
– agromek
22 hours ago
the set of B matrices is the subspace of R^3
– agromek
22 hours ago
No, I don't think so.
– Richard Martin
22 hours ago
No, I don't think so.
– Richard Martin
22 hours ago
the whole task was that I have two 3x3 matrices: A and C - A has rank 2 and C can be any 3x3 matrix and the question is: what is the basis of a subspace of the space of all 3x3 matrices that is generated by the set of 3x3 matrices B that satisfy the equation A*C=B (I'm trying to translate it into english as exact as I can)
– agromek
22 hours ago
the whole task was that I have two 3x3 matrices: A and C - A has rank 2 and C can be any 3x3 matrix and the question is: what is the basis of a subspace of the space of all 3x3 matrices that is generated by the set of 3x3 matrices B that satisfy the equation A*C=B (I'm trying to translate it into english as exact as I can)
– agromek
22 hours ago
maybe I'm interpreting the phrase "the space of all 3x3 matrices" wrongly, I thought it is just R^3 but maybe it's something else?
– agromek
22 hours ago
maybe I'm interpreting the phrase "the space of all 3x3 matrices" wrongly, I thought it is just R^3 but maybe it's something else?
– agromek
22 hours ago
The space of all 3x3 matrices acts on $mathbb R^3$ but it is not of itself $mathbb R^3$.
– Richard Martin
22 hours ago
The space of all 3x3 matrices acts on $mathbb R^3$ but it is not of itself $mathbb R^3$.
– Richard Martin
22 hours ago
|
show 2 more comments
up vote
0
down vote
The vector space of all $3 x 3$ matrices is not $R^3$. You can verify that the space has dimension $9$ because you will need $9$ vectors for a basis. Probably the most likely ones would be $begin{bmatrix}1 & 0 & 0\0 & 0 & 0\0 & 0 & 0end{bmatrix}$, $begin{bmatrix}0 & 1 & 0\0 & 0 & 0\0 & 0 & 0end{bmatrix}$ ... $begin{bmatrix}0 & 0 & 1\0 & 0 & 0\0 & 0 & 0end{bmatrix}$,$begin{bmatrix}0 & 0 & 0\1 & 0 & 0\0 & 0 & 0end{bmatrix}$, $begin{bmatrix}0 & 0 & 0\0 & 1 & 0\0 & 0 & 0end{bmatrix}$, $begin{bmatrix}0 & 0 & 0\0 & 0 & 1\0 & 0 & 0end{bmatrix}$,$begin{bmatrix}0 & 0 & 0\0 & 0 & 0\1 & 0 & 0end{bmatrix}$, $begin{bmatrix}0 & 0 & 0\0 & 0 & 0\0 & 1 & 0end{bmatrix}$, $begin{bmatrix}0 & 0 & 0\0 & 0 & 0\0 & 0 & 1end{bmatrix}$
Now considering that your subspace only contains matrices with rank $leq2$ the basis for that space will contain only $6$ of these $9$.
answered 20 hours ago
Chai
1012
New contributor
Chai is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
SInce all those matrices have rank $le2$, they all belong to the given set.
– egreg
20 hours ago
Is that true? Taking linear combinations of all $9$ will yield all possible matrices, including rank $3$ ones. If we leave out the ones that have 1's in the last column ofr instance, all combinations will have rank $leq2$ , or am I missing something?
– Chai
20 hours ago
Well, every matrix belongs to the span of the rank $1$ matrices.
– egreg
20 hours ago
I'm not quite sure what you mean by that. As I understand it, OP is looking for a basis of the subspace of $3x3$ matrices that do not include the ones with rank$3$. I believe you could find a basis in this manner. But if I am wrong I'd like to learn as well !
– Chai
20 hours ago
I don't really understand why the vector space of all 3x3 matrices has dimension 9? can someone please explain?
– agromek
16 hours ago
|
show 3 more comments
up vote
0
down vote
The vector space of all $3 x 3$ matrices is not $R^3$. You can verify that the space has dimension $9$ because you will need $9$ vectors for a basis. Probably the most likely ones would be $begin{bmatrix}1 & 0 & 0\0 & 0 & 0\0 & 0 & 0end{bmatrix}$, $begin{bmatrix}0 & 1 & 0\0 & 0 & 0\0 & 0 & 0end{bmatrix}$ ... $begin{bmatrix}0 & 0 & 1\0 & 0 & 0\0 & 0 & 0end{bmatrix}$,$begin{bmatrix}0 & 0 & 0\1 & 0 & 0\0 & 0 & 0end{bmatrix}$, $begin{bmatrix}0 & 0 & 0\0 & 1 & 0\0 & 0 & 0end{bmatrix}$, $begin{bmatrix}0 & 0 & 0\0 & 0 & 1\0 & 0 & 0end{bmatrix}$,$begin{bmatrix}0 & 0 & 0\0 & 0 & 0\1 & 0 & 0end{bmatrix}$, $begin{bmatrix}0 & 0 & 0\0 & 0 & 0\0 & 1 & 0end{bmatrix}$, $begin{bmatrix}0 & 0 & 0\0 & 0 & 0\0 & 0 & 1end{bmatrix}$
Now considering that your subspace only contains matrices with rank $leq2$ the basis for that space will contain only $6$ of these $9$.
answered 20 hours ago
Chai
1012
New contributor
Chai is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
SInce all those matrices have rank $le2$, they all belong to the given set.
– egreg
20 hours ago
Is that true? Taking linear combinations of all $9$ will yield all possible matrices, including rank $3$ ones. If we leave out the ones that have 1's in the last column ofr instance, all combinations will have rank $leq2$ , or am I missing something?
– Chai
20 hours ago
Well, every matrix belongs to the span of the rank $1$ matrices.
– egreg
20 hours ago
I'm not quite sure what you mean by that. As I understand it, OP is looking for a basis of the subspace of $3x3$ matrices that do not include the ones with rank$3$. I believe you could find a basis in this manner. But if I am wrong I'd like to learn as well !
– Chai
20 hours ago
I don't really understand why the vector space of all 3x3 matrices has dimension 9? can someone please explain?
– agromek
16 hours ago
|
show 3 more comments
up vote
0
down vote
up vote
0
down vote
The vector space of all $3 x 3$ matrices is not $R^3$. You can verify that the space has dimension $9$ because you will need $9$ vectors for a basis. Probably the most likely ones would be $begin{bmatrix}1 & 0 & 0\0 & 0 & 0\0 & 0 & 0end{bmatrix}$, $begin{bmatrix}0 & 1 & 0\0 & 0 & 0\0 & 0 & 0end{bmatrix}$ ... $begin{bmatrix}0 & 0 & 1\0 & 0 & 0\0 & 0 & 0end{bmatrix}$,$begin{bmatrix}0 & 0 & 0\1 & 0 & 0\0 & 0 & 0end{bmatrix}$, $begin{bmatrix}0 & 0 & 0\0 & 1 & 0\0 & 0 & 0end{bmatrix}$, $begin{bmatrix}0 & 0 & 0\0 & 0 & 1\0 & 0 & 0end{bmatrix}$,$begin{bmatrix}0 & 0 & 0\0 & 0 & 0\1 & 0 & 0end{bmatrix}$, $begin{bmatrix}0 & 0 & 0\0 & 0 & 0\0 & 1 & 0end{bmatrix}$, $begin{bmatrix}0 & 0 & 0\0 & 0 & 0\0 & 0 & 1end{bmatrix}$
Now considering that your subspace only contains matrices with rank $leq2$ the basis for that space will contain only $6$ of these $9$.
answered 20 hours ago
Chai
1012
New contributor
Chai is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
The vector space of all $3 x 3$ matrices is not $R^3$. You can verify that the space has dimension $9$ because you will need $9$ vectors for a basis. Probably the most likely ones would be $begin{bmatrix}1 & 0 & 0\0 & 0 & 0\0 & 0 & 0end{bmatrix}$, $begin{bmatrix}0 & 1 & 0\0 & 0 & 0\0 & 0 & 0end{bmatrix}$ ... $begin{bmatrix}0 & 0 & 1\0 & 0 & 0\0 & 0 & 0end{bmatrix}$,$begin{bmatrix}0 & 0 & 0\1 & 0 & 0\0 & 0 & 0end{bmatrix}$, $begin{bmatrix}0 & 0 & 0\0 & 1 & 0\0 & 0 & 0end{bmatrix}$, $begin{bmatrix}0 & 0 & 0\0 & 0 & 1\0 & 0 & 0end{bmatrix}$,$begin{bmatrix}0 & 0 & 0\0 & 0 & 0\1 & 0 & 0end{bmatrix}$, $begin{bmatrix}0 & 0 & 0\0 & 0 & 0\0 & 1 & 0end{bmatrix}$, $begin{bmatrix}0 & 0 & 0\0 & 0 & 0\0 & 0 & 1end{bmatrix}$
Now considering that your subspace only contains matrices with rank $leq2$ the basis for that space will contain only $6$ of these $9$.
answered 20 hours ago
Chai
1012
New contributor
Chai is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 13 hours ago
answered 20 hours ago
Chai
1012
New contributor
Chai is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
answered 20 hours ago
Chai
1012
answered 20 hours ago
Chai
1012
1012
New contributor
Chai is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Chai is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Chai is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
SInce all those matrices have rank $le2$, they all belong to the given set.
– egreg
20 hours ago
Is that true? Taking linear combinations of all $9$ will yield all possible matrices, including rank $3$ ones. If we leave out the ones that have 1's in the last column ofr instance, all combinations will have rank $leq2$ , or am I missing something?
– Chai
20 hours ago
Well, every matrix belongs to the span of the rank $1$ matrices.
– egreg
20 hours ago
I'm not quite sure what you mean by that. As I understand it, OP is looking for a basis of the subspace of $3x3$ matrices that do not include the ones with rank$3$. I believe you could find a basis in this manner. But if I am wrong I'd like to learn as well !
– Chai
20 hours ago
I don't really understand why the vector space of all 3x3 matrices has dimension 9? can someone please explain?
– agromek
16 hours ago
|
show 3 more comments
SInce all those matrices have rank $le2$, they all belong to the given set.
– egreg
20 hours ago
Is that true? Taking linear combinations of all $9$ will yield all possible matrices, including rank $3$ ones. If we leave out the ones that have 1's in the last column ofr instance, all combinations will have rank $leq2$ , or am I missing something?
– Chai
20 hours ago
Well, every matrix belongs to the span of the rank $1$ matrices.
– egreg
20 hours ago
I'm not quite sure what you mean by that. As I understand it, OP is looking for a basis of the subspace of $3x3$ matrices that do not include the ones with rank$3$. I believe you could find a basis in this manner. But if I am wrong I'd like to learn as well !
– Chai
20 hours ago
I don't really understand why the vector space of all 3x3 matrices has dimension 9? can someone please explain?
– agromek
16 hours ago
SInce all those matrices have rank $le2$, they all belong to the given set.
– egreg
20 hours ago
SInce all those matrices have rank $le2$, they all belong to the given set.
– egreg
20 hours ago
Is that true? Taking linear combinations of all $9$ will yield all possible matrices, including rank $3$ ones. If we leave out the ones that have 1's in the last column ofr instance, all combinations will have rank $leq2$ , or am I missing something?
– Chai
20 hours ago
Is that true? Taking linear combinations of all $9$ will yield all possible matrices, including rank $3$ ones. If we leave out the ones that have 1's in the last column ofr instance, all combinations will have rank $leq2$ , or am I missing something?
– Chai
20 hours ago
Well, every matrix belongs to the span of the rank $1$ matrices.
– egreg
20 hours ago
Well, every matrix belongs to the span of the rank $1$ matrices.
– egreg
20 hours ago
I'm not quite sure what you mean by that. As I understand it, OP is looking for a basis of the subspace of $3x3$ matrices that do not include the ones with rank$3$. I believe you could find a basis in this manner. But if I am wrong I'd like to learn as well !
– Chai
20 hours ago
I'm not quite sure what you mean by that. As I understand it, OP is looking for a basis of the subspace of $3x3$ matrices that do not include the ones with rank$3$. I believe you could find a basis in this manner. But if I am wrong I'd like to learn as well !
– Chai
20 hours ago
I don't really understand why the vector space of all 3x3 matrices has dimension 9? can someone please explain?
– agromek
16 hours ago
I don't really understand why the vector space of all 3x3 matrices has dimension 9? can someone please explain?
– agromek
16 hours ago
|
show 3 more comments
agromek is a new contributor. Be nice, and check out our Code of Conduct.
agromek is a new contributor. Be nice, and check out our Code of Conduct.
agromek is a new contributor. Be nice, and check out our Code of Conduct.
agromek is a new contributor. Be nice, and check out our Code of Conduct.
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Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
– José Carlos Santos
22 hours ago