Prove that the set S1 of symmetric matrices and the set S2 the anti-symmetric matrices nxn are vector subspaces of the Mnxm and that it has Mnxm = S1 + S2
Prove that the set S1 of symmetric matrices and the set S2 the anti-symmetric matrices nxn are vector subspaces of the Mnxm and that it has Mnxm = S1 + S2
let be the vector space of all matrices over the field if then for any we have: i.e.
so is a vector space. do the same for to show that if of course, let and put: and see that and
which proves that note that since we actually have: