The Sylvester Rank Inequality
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- čas přidán 11. 09. 2024
- 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
I have no idea how I got recommended this video but I enjoyed it at least without understanding anything of it
Same... I don't know what nullity is !