"A matrix A is a symmetric matrix if its transpose AT = A." This is my definition.
"A square matrix A is a symmetric matrix if its transpose AT = A." This is the textbook definition.
I understand that only square matrices can be symmetric, but I figured it would be all right to cut out the "square", as satisfying the equation AT = A would ensure it is a square matrix.
So why can't I omit the "square"? (An error I was sternly reminded of.)
Any better definitions would also be greatly appreciated.
