a b For a general matrix A we can see that A + AZ is a C d symmetric matrix; while A - AT - is a skew-symmetric matrix Now since A - - (A + A" ) + -(A - A" ), we can deduce that every square matrix A can be written as O the sum of two symmetric matrices the sum of a symmetric and a skew-symmetric matrix O the sum of two skew-symmetric matrices Note: . the Maple notation for the matrix a b d is , > . include a space between the less than symbol