math
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.
Let
A be a skew symmetric matrix.
By the definition of skewsymmetry,
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