Question

Wanted to ask a question about column spaces...suppose A and B are both nonnegative definite matrix with same order, how can I prove
c(A) belongs to c(A+B)....

Answer 1

Try looking at the null spaces of A and A+B, which (for symmetric A and B) are orthogonal to the column spaces. If N(A+B) is contained in N(A), then C(A) is contained in C(A+B).