posted by kevin on .
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.
Let a(i,j) stand for the element of A on the ith row and jth column.
A be a skew symmetric matrix.
By the definition of skew-symmetry,
On the diagonal,
since x=-x => x=0