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Math Help - Vector spaces-subspace

  1. #1
    Junior Member maths900's Avatar
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    Vector spaces-subspace

    V= {B \in M_{n}(R). B is skew symmetric.}

    How can i show V is a subspace of M_{n}(R)?
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  2. #2
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    Quote Originally Posted by maths900 View Post
    V= {B \in M_{n}(R). B is skew symmetric.} How can i show V is a subspace of M_{n}(R)?
    Do you know that 0 \in V?
    Can you show that \left\{ {C,D} \right\} \subset V\;\& \;s \in \Re \; \Rightarrow \;C + sD \in V?
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  3. #3
    Junior Member maths900's Avatar
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    Quote Originally Posted by Plato View Post
    Do you know that 0 \in V?
    Can you show that \left\{ {C,D} \right\} \subset V\;\& \;s \in \Re \; \Rightarrow \;C + sD \in V?
    Sorry can you explain what you have written. Thanks.
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  4. #4
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    What about my answer do you not understand?
    What does your textbook say about subspaces of vector spaces?
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  5. #5
    Junior Member maths900's Avatar
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    Quote Originally Posted by Plato View Post
    What about my answer do you not understand?
    What does your textbook say about subspaces of vector spaces?
    All of it
    My lecture notes show that for it to be a subspace it has to satisfy three axioms.
    I know that 0 belongs to V, but how would i apply that to skew symmetric matrices?
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  6. #6
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    Quote Originally Posted by maths900 View Post
    All of it
    My lecture notes show that for it to be a subspace it has to satisfy three axioms.
    I know that 0 belongs to V, but how would i apply that to skew symmetric matrices?
    Is the sum of two of skew symmetric matrices a skew symmetric matrix?
    If you multiply a skew symmetric matrix by a real number do you get a symmetric matrix?
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  7. #7
    Junior Member maths900's Avatar
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    Lol yea of course, i understand that now.

    How do i go about starting it? Shall i introduce a skew symmetric matrix/matrices??
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  8. #8
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    Quote Originally Posted by maths900 View Post
    How do i go about starting it? Shall i introduce a skew symmetric matrix/matrices??
    What do you know about skew symmetric matrix/matrices?
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  9. #9
    Junior Member maths900's Avatar
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    Quote Originally Posted by Plato View Post
    What do you know about skew symmetric matrix/matrices?
    B transposed = -B, is that correct?
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  10. #10
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    Quote Originally Posted by maths900 View Post
    B transposed = -B, is that correct?
    Yes. Now answer the two question.
    Is the sum of two of skew symmetric matrices a skew symmetric matrix?
    If you multiply a skew symmetric matrix by a real number do you get a symmetric matrix?
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  11. #11
    Junior Member maths900's Avatar
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    Quote Originally Posted by Plato View Post
    Yes. Now answer the two question.
    Is the sum of two of skew symmetric matrices a skew symmetric matrix?
    If you multiply a skew symmetric matrix by a real number do you get a symmetric matrix?
    Yes i do
    How can I show V is not an empty set....1st axiom

    EDIT: Lol its pretty obvious now. I just have to write down any skew symmetric matric i guess. Thanks. You made it sound much easier.
    Last edited by maths900; February 17th 2009 at 09:50 AM.
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  12. #12
    Junior Member maths900's Avatar
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    Will its dimension be 2n or n^2?
    Last edited by maths900; February 17th 2009 at 10:17 AM.
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