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I have a small question. Is it necessary for an anti-symmetric matrix to have a 0's diagonal ?

I have this question about the dimension of 2x2 symmetric matrices vs. dimension of anti-symmetric 2x2 matrices.

The solution is that the dim(symmetric) is 3 while dim(anti-symmetric) is 1, illustrated by a matrix with a zero diagonal.

anti-symmetric is when A=-transpose(A), will only a 0's diagonal satisfy this ?

thanks !