A matrix A Mat n R is symmetric if A = A t and skew-symmetric if

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A matrix A ϵ Mat_nR is symmetric if A = A^t and skew-symmetric if A = -A^t.

(a) If A and B are [skew] symmetric, then A +B is [skew] symmetric.

(b) Let R be commutative. If A,B are symmetric, then AB is symmetric if and only if AB = BA. Also show that for any matrix B ϵ Mat_nR,BB^t and B + B^t are symmetric and B - B^t is skew-symmetric.

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Algebra Graduate Texts In Mathematics 73

ISBN: 9780387905181

8th Edition

Authors: Thomas W. Hungerford

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A matrix A Mat n R is symmetric if A = A t and skew-symmetric if

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a If A and B are skew symmetric then A B is skew symmetric This statement is true Lets consider the ...View the full answer

Algebra Graduate Texts In Mathematics 73

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