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Math Help - Skew Symmetric Matrix

  1. #1
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    Skew Symmetric Matrix

    Hi,

    I would like some guidance on how to approach this question please:

    Question: Let B be an n*n skew symmetric matrix and let A = I + B. Show that AA^T = (I+B)(I-B)= A^TA
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  2. #2
    Senior Member Sambit's Avatar
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    If B is a skew symmetric matrix, then B^T=-B. And AA^T=(I+B)(I+B)^T=(I+B)(I^T+B^T). Using the property of skew symmetric matrix as stated, you should be able to work it out now.
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  3. #3
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    Thanks for your reply Sambit.

    I am still trying to figure out how you got AA^T = (I + B)(I + B)^T

    Here is what I understand so far:

    B^T= -B (this is the definition of a skew symmetric matrix)

    A = I + B (this is given)

    If A = I + B, then A^T = -A = I - B (does this make any sense?)

    Therefore, AA^T = (I+B)(I-B) (is this correct?)
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  4. #4
    Senior Member Sambit's Avatar
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    Quote Originally Posted by sparky View Post

    If A = I + B, then A^T = -A = I - B
    This final result is correct, but not the intermediate step. It comes as follows: A^T=(I+B)^T=(I^T+B^T)=(I+B^T)=(I-B) But note that A^T \neq -A since A is not mentioned as a skew-symmetric matrix.
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  5. #5
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    Thanks Sambit
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