C(a)<c(a+b)

[xihashiwo]

Hello,

I have a question. If A and B are NND matrices, how to prove C(A) belongs to C(A+B)?

I can prove that C(A)<C(A,B) by using A=(A,B)transpose[(I,0)], and I also can prove C(A+B)<C(A,B) using the similar approach.

But I cannot move further because my thoughs maybe not related to the answer at all.

Can someone help? Many thanks.

[yenchin]

You need to explain your notation. What's NND? what's "C" ?

[xihashiwo]

NND is nonnegative definite, C is column space

[Mark44]

Also, I get that C(A + B) is the column space of the matrix sum, A + B, but what does C(A, B) mean? And this - (A,B)transpose[(I,0)].

[xihashiwo]

Please no worry about those stuff, I am just confused about my original question, why C(A) belongs to C(A+B), is there any tricks?

Also, I get that C(A + B) is the column space of the matrix sum, A + B, but what does C(A, B) mean? And this - (A,B)transpose[(I,0)].