Page "Symmetric matrix" Paragraph 16

Let Mat < sub > n </ sub > denote the space of matrices.

A symmetric n × n matrix is determined by n ( n + 1 )/ 2 scalars ( the number of entries on or above the main diagonal ).

Similarly, a skew-symmetric matrix is determined by n ( n − 1 )/ 2 scalars ( the number of entries above the main diagonal ).

If Sym < sub > n </ sub > denotes the space of symmetric matrices and Skew < sub > n </ sub > the space of skew-symmetric matrices then since and