The Sylvester Rank Inequality

We prove the Sylvester Rank Inequality. This asserts that if A is an mxk matrix and B is a kxn matrix, then rank(A) + rank(B) is no more than k + rank(AB). This Inequality is proven using the Rank-Nullity Theorem along with an inequality for nullity(AB) in terms nullity(A) and nullity(B). This result gives us good information about the range of factorizations for non-square matrices.
#mikethemathematician, #mikedabkowski, #profdabkowski

[@Swishsy]

I have no idea how I got recommended this video but I enjoyed it at least without understanding anything of it

[@siddharthchauhan1129]

Same... I don't know what nullity is !