Posted by **kevin** on Tuesday, January 11, 2011 at 5:54am.

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 -
**MathMate**, Tuesday, January 11, 2011 at 7:31pm
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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