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inknit
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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.
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.