# Show that diagonal entries of a skew symmetric matrix are zero.

by inknit
Tags: diagonal, entries, matrix, skew, symmetric
 P: 59 I'm pretty inexperienced in proof writing. So not sure if this was valid. If a matrix is skew symmetric then A^T = - A, that is the transpose of A is equal to negative A. This implies that if A = a(i,j), then a(j,i) = -a(i,j). If we're referring to diagonal entries, we can say a(j,j) = -a(j,j). The only way for this to be true is if a(j,j) = 0. So therefore all the diagonal entries of a skew symmetric matrix are 0. Is this good enough? Thanks.
 HW Helper P: 6,202 I think it would work as a valid proof.
P: 3
 Quote by inknit I'm pretty inexperienced in proof writing. So not sure if this was valid. If a matrix is skew symmetric then A^T = - A, that is the transpose of A is equal to negative A. This implies that if A = a(i,j), then a(j,i) = -a(i,j). If we're referring to diagonal entries, we can say a(j,j) = -a(j,j). The only way for this to be true is if a(j,j) = 0. So therefore all the diagonal entries of a skew symmetric matrix are 0. Is this good enough? Thanks.
It's great. Thanks!

Math
Emeritus