symmetric matrix
a symmetric matrix is called symmetric if it equals its transpose.
[cite:;taken from @algebra_axler_2024 definition 9.11 symmetric matrix]
[cite:;taken from @algebra_axler_2024 definition 9.11 symmetric matrix]
a matrix 
is antisymmetric if
or
where 
denotes the element of at the 
th row and the 
th column.
is antisymmetric iforwhere denotes the element of at the th row and the th column.