Question

Hello,

Is there any theorem for the rank of the product of two matrices A,B (both of them are nxn dimension)?

I mean something like rank(AB) = rank(BA) when A,B matrices are of the same dimension nxn?

Answer 1

I think you already know these, but what I can remember is that, if B is a matrix n-by-k:
rank(AB) = min(rank(A), rank(B))
If B has rank n, then:
rank(AB) = rank(A)
and if C is a matrix k-by-m with rank m:
rank(CA) = rank(A).
Sorry if you already know these, LA is not my strong subject :-)

Answer 2

I've found these properties of rank at wikipedia, already!
Thanks for answering, though :-)

Answer 3

No problem :-)