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Dimensions of Subspace [closed]
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Suppose $V$ is a subspace of $mathbbR^3 times 3$ consisting of skew-symmetric diagonal matrices. What is $mathrmdim ; V$?
The skew-symmetric matrix implies that the transpose of the matrix is its negative. I.e $A^top = -A$.
Taking into account that $A$ may be a diagonal skewed matrix, how does that determine the dimension of $V$. Would $dim V$ simply be 3...
linear-algebra matrices vector-spaces
edited Jul 21 at 13:24
Nik Pronko
795717
asked Jul 21 at 12:32
KhanMan
447
closed as off-topic by John Ma, Mostafa Ayaz, Strants, Taroccoesbrocco, Xander Henderson Jul 25 at 0:08
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – John Ma, Mostafa Ayaz, Strants, Taroccoesbrocco, Xander Henderson
add a comment |Â
up vote
-2
down vote
favorite
Suppose $V$ is a subspace of $mathbbR^3 times 3$ consisting of skew-symmetric diagonal matrices. What is $mathrmdim ; V$?
The skew-symmetric matrix implies that the transpose of the matrix is its negative. I.e $A^top = -A$.
Taking into account that $A$ may be a diagonal skewed matrix, how does that determine the dimension of $V$. Would $dim V$ simply be 3...
linear-algebra matrices vector-spaces
edited Jul 21 at 13:24
Nik Pronko
795717
asked Jul 21 at 12:32
KhanMan
447
closed as off-topic by John Ma, Mostafa Ayaz, Strants, Taroccoesbrocco, Xander Henderson Jul 25 at 0:08
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – John Ma, Mostafa Ayaz, Strants, Taroccoesbrocco, Xander Henderson
Welcome to math.s, KhanMan. You should use mathjax to format your math, see latex4technics.com.
– Nik Pronko
Jul 21 at 12:53
Hint: try to find two different $3times3$ skew-symmetric diagonal matrices.
– Gerry Myerson
Jul 21 at 13:27
add a comment |Â
up vote
-2
down vote
favorite
up vote
-2
down vote
favorite
Suppose $V$ is a subspace of $mathbbR^3 times 3$ consisting of skew-symmetric diagonal matrices. What is $mathrmdim ; V$?
The skew-symmetric matrix implies that the transpose of the matrix is its negative. I.e $A^top = -A$.
Taking into account that $A$ may be a diagonal skewed matrix, how does that determine the dimension of $V$. Would $dim V$ simply be 3...
linear-algebra matrices vector-spaces
edited Jul 21 at 13:24
Nik Pronko
795717
asked Jul 21 at 12:32
KhanMan
447
Suppose $V$ is a subspace of $mathbbR^3 times 3$ consisting of skew-symmetric diagonal matrices. What is $mathrmdim ; V$?
The skew-symmetric matrix implies that the transpose of the matrix is its negative. I.e $A^top = -A$.
Taking into account that $A$ may be a diagonal skewed matrix, how does that determine the dimension of $V$. Would $dim V$ simply be 3...
linear-algebra matrices vector-spaces
edited Jul 21 at 13:24
Nik Pronko
795717
asked Jul 21 at 12:32
KhanMan
447
edited Jul 21 at 13:24
Nik Pronko
795717
edited Jul 21 at 13:24
Nik Pronko
795717
edited Jul 21 at 13:24
Nik Pronko
795717
795717
asked Jul 21 at 12:32
KhanMan
447
asked Jul 21 at 12:32
KhanMan
447
asked Jul 21 at 12:32
KhanMan
447
447
closed as off-topic by John Ma, Mostafa Ayaz, Strants, Taroccoesbrocco, Xander Henderson Jul 25 at 0:08
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – John Ma, Mostafa Ayaz, Strants, Taroccoesbrocco, Xander Henderson
closed as off-topic by John Ma, Mostafa Ayaz, Strants, Taroccoesbrocco, Xander Henderson Jul 25 at 0:08
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – John Ma, Mostafa Ayaz, Strants, Taroccoesbrocco, Xander Henderson
Welcome to math.s, KhanMan. You should use mathjax to format your math, see latex4technics.com.
– Nik Pronko
Jul 21 at 12:53
Hint: try to find two different $3times3$ skew-symmetric diagonal matrices.
– Gerry Myerson
Jul 21 at 13:27
add a comment |Â
Welcome to math.s, KhanMan. You should use mathjax to format your math, see latex4technics.com.
– Nik Pronko
Jul 21 at 12:53
Hint: try to find two different $3times3$ skew-symmetric diagonal matrices.
– Gerry Myerson
Jul 21 at 13:27
Welcome to math.s, KhanMan. You should use mathjax to format your math, see latex4technics.com.
– Nik Pronko
Jul 21 at 12:53
Welcome to math.s, KhanMan. You should use mathjax to format your math, see latex4technics.com.
– Nik Pronko
Jul 21 at 12:53
Hint: try to find two different $3times3$ skew-symmetric diagonal matrices.
– Gerry Myerson
Jul 21 at 13:27
Hint: try to find two different $3times3$ skew-symmetric diagonal matrices.
– Gerry Myerson
Jul 21 at 13:27
add a comment |Â
2 Answers
2
active
oldest
votes
up vote
2
down vote
accepted
To properly answer the question, you need to find a basis for skew symmetric matrices. All such matrix is of the form
$$pmatrix0&a&b\ -a&0&c\-b&-c&0$$
A basis would consist of specific such matrices for $(a=1,,b=c=0)$, $ (b=1,,a=c=0)$ and $(c=1,,a=b=0)$.
answered Jul 21 at 13:27
Berci
56.4k23570
is their a generalized form for skew-symmetric DIAGONAL matrices?
– KhanMan
Jul 22 at 1:28
2
Hey, KhanMan, did you not see the comment I left on your question? Can you find as many as two different skew-symmetric diagonal matrices? Look, I'll even spot you one: the zero matrix is diagonal and skew-symmetric. Now: can you find even one more?
– Gerry Myerson
Jul 22 at 4:05
1
Are you still here, KhanMan?
– Gerry Myerson
Jul 23 at 5:50
@GerryMyerson Got it! Thanks
– KhanMan
Jul 24 at 22:44
add a comment |Â
up vote
0
down vote
Since it is diagonal the $dim V$ is at most $3$. Also skew-symmetry imposes that$$A^T=-A$$since $A$ is diagonal we have $A^T=A$ therefore $$A=-A$$ or $$A=0$$which means that $$Large dim V=0$$
answered Jul 24 at 14:30
Mostafa Ayaz
8,5773630
add a comment |Â
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
2
down vote
accepted
To properly answer the question, you need to find a basis for skew symmetric matrices. All such matrix is of the form
$$pmatrix0&a&b\ -a&0&c\-b&-c&0$$
A basis would consist of specific such matrices for $(a=1,,b=c=0)$, $ (b=1,,a=c=0)$ and $(c=1,,a=b=0)$.
answered Jul 21 at 13:27
Berci
56.4k23570
is their a generalized form for skew-symmetric DIAGONAL matrices?
– KhanMan
Jul 22 at 1:28
2
Hey, KhanMan, did you not see the comment I left on your question? Can you find as many as two different skew-symmetric diagonal matrices? Look, I'll even spot you one: the zero matrix is diagonal and skew-symmetric. Now: can you find even one more?
– Gerry Myerson
Jul 22 at 4:05
1
Are you still here, KhanMan?
– Gerry Myerson
Jul 23 at 5:50
@GerryMyerson Got it! Thanks
– KhanMan
Jul 24 at 22:44
add a comment |Â
up vote
2
down vote
accepted
To properly answer the question, you need to find a basis for skew symmetric matrices. All such matrix is of the form
$$pmatrix0&a&b\ -a&0&c\-b&-c&0$$
A basis would consist of specific such matrices for $(a=1,,b=c=0)$, $ (b=1,,a=c=0)$ and $(c=1,,a=b=0)$.
answered Jul 21 at 13:27
Berci
56.4k23570
is their a generalized form for skew-symmetric DIAGONAL matrices?
– KhanMan
Jul 22 at 1:28
2
Hey, KhanMan, did you not see the comment I left on your question? Can you find as many as two different skew-symmetric diagonal matrices? Look, I'll even spot you one: the zero matrix is diagonal and skew-symmetric. Now: can you find even one more?
– Gerry Myerson
Jul 22 at 4:05
1
Are you still here, KhanMan?
– Gerry Myerson
Jul 23 at 5:50
@GerryMyerson Got it! Thanks
– KhanMan
Jul 24 at 22:44
add a comment |Â
up vote
2
down vote
accepted
up vote
2
down vote
accepted
To properly answer the question, you need to find a basis for skew symmetric matrices. All such matrix is of the form
$$pmatrix0&a&b\ -a&0&c\-b&-c&0$$
A basis would consist of specific such matrices for $(a=1,,b=c=0)$, $ (b=1,,a=c=0)$ and $(c=1,,a=b=0)$.
answered Jul 21 at 13:27
Berci
56.4k23570
To properly answer the question, you need to find a basis for skew symmetric matrices. All such matrix is of the form
$$pmatrix0&a&b\ -a&0&c\-b&-c&0$$
A basis would consist of specific such matrices for $(a=1,,b=c=0)$, $ (b=1,,a=c=0)$ and $(c=1,,a=b=0)$.
answered Jul 21 at 13:27
Berci
56.4k23570
answered Jul 21 at 13:27
Berci
56.4k23570
answered Jul 21 at 13:27
Berci
56.4k23570
answered Jul 21 at 13:27
Berci
56.4k23570
56.4k23570
is their a generalized form for skew-symmetric DIAGONAL matrices?
– KhanMan
Jul 22 at 1:28
2
Hey, KhanMan, did you not see the comment I left on your question? Can you find as many as two different skew-symmetric diagonal matrices? Look, I'll even spot you one: the zero matrix is diagonal and skew-symmetric. Now: can you find even one more?
– Gerry Myerson
Jul 22 at 4:05
1
Are you still here, KhanMan?
– Gerry Myerson
Jul 23 at 5:50
@GerryMyerson Got it! Thanks
– KhanMan
Jul 24 at 22:44
add a comment |Â
is their a generalized form for skew-symmetric DIAGONAL matrices?
– KhanMan
Jul 22 at 1:28
2
Hey, KhanMan, did you not see the comment I left on your question? Can you find as many as two different skew-symmetric diagonal matrices? Look, I'll even spot you one: the zero matrix is diagonal and skew-symmetric. Now: can you find even one more?
– Gerry Myerson
Jul 22 at 4:05
1
Are you still here, KhanMan?
– Gerry Myerson
Jul 23 at 5:50
@GerryMyerson Got it! Thanks
– KhanMan
Jul 24 at 22:44
is their a generalized form for skew-symmetric DIAGONAL matrices?
– KhanMan
Jul 22 at 1:28
is their a generalized form for skew-symmetric DIAGONAL matrices?
– KhanMan
Jul 22 at 1:28
2
2
Hey, KhanMan, did you not see the comment I left on your question? Can you find as many as two different skew-symmetric diagonal matrices? Look, I'll even spot you one: the zero matrix is diagonal and skew-symmetric. Now: can you find even one more?
– Gerry Myerson
Jul 22 at 4:05
Hey, KhanMan, did you not see the comment I left on your question? Can you find as many as two different skew-symmetric diagonal matrices? Look, I'll even spot you one: the zero matrix is diagonal and skew-symmetric. Now: can you find even one more?
– Gerry Myerson
Jul 22 at 4:05
1
1
Are you still here, KhanMan?
– Gerry Myerson
Jul 23 at 5:50
Are you still here, KhanMan?
– Gerry Myerson
Jul 23 at 5:50
@GerryMyerson Got it! Thanks
– KhanMan
Jul 24 at 22:44
@GerryMyerson Got it! Thanks
– KhanMan
Jul 24 at 22:44
add a comment |Â
up vote
0
down vote
Since it is diagonal the $dim V$ is at most $3$. Also skew-symmetry imposes that$$A^T=-A$$since $A$ is diagonal we have $A^T=A$ therefore $$A=-A$$ or $$A=0$$which means that $$Large dim V=0$$
answered Jul 24 at 14:30
Mostafa Ayaz
8,5773630
add a comment |Â
up vote
0
down vote
Since it is diagonal the $dim V$ is at most $3$. Also skew-symmetry imposes that$$A^T=-A$$since $A$ is diagonal we have $A^T=A$ therefore $$A=-A$$ or $$A=0$$which means that $$Large dim V=0$$
answered Jul 24 at 14:30
Mostafa Ayaz
8,5773630
add a comment |Â
up vote
0
down vote
up vote
0
down vote
Since it is diagonal the $dim V$ is at most $3$. Also skew-symmetry imposes that$$A^T=-A$$since $A$ is diagonal we have $A^T=A$ therefore $$A=-A$$ or $$A=0$$which means that $$Large dim V=0$$
answered Jul 24 at 14:30
Mostafa Ayaz
8,5773630
Since it is diagonal the $dim V$ is at most $3$. Also skew-symmetry imposes that$$A^T=-A$$since $A$ is diagonal we have $A^T=A$ therefore $$A=-A$$ or $$A=0$$which means that $$Large dim V=0$$
answered Jul 24 at 14:30
Mostafa Ayaz
8,5773630
answered Jul 24 at 14:30
Mostafa Ayaz
8,5773630
answered Jul 24 at 14:30
Mostafa Ayaz
8,5773630
answered Jul 24 at 14:30
Mostafa Ayaz
8,5773630
8,5773630
add a comment |Â
add a comment |Â
Welcome to math.s, KhanMan. You should use mathjax to format your math, see latex4technics.com.
– Nik Pronko
Jul 21 at 12:53
Hint: try to find two different $3times3$ skew-symmetric diagonal matrices.
– Gerry Myerson
Jul 21 at 13:27