Question: recall that a square matrix a is 1 symmetric if...
Recall that a square matrix A is (1) symmetric if A^T = A, and (2) skew-symmetric if A^T = −A.
What are the dimensions of the following vector spaces? Justify your answers.
a) The space S, of all 3 × 3 symmetric matrices?
b) The space T , of all 3 × 3 skew-symmetric matrices?
c) The space S ∩ T ?
d) The space S + T ? What familiar vector space is this?