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math

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A matrix A is said to be skew symmetric if A^T = -A. Show that is a matrix is skew symmetric then its diagonal entries must all be 0.

A^T meant to be A transpose.

  • math -

    Let a(i,j) stand for the element of A on the ith row and jth column.

    Let
    A be a skew symmetric matrix.

    By the definition of skew-symmetry,
    a(j,i)=-a(i,j)

    On the diagonal,
    i=j
    => a(i,i)=-a(i,i)
    => a(i,i)=0

    since x=-x => x=0

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