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
Watch video The Sylvester Rank Inequality online, duration hours minute second in high quality that is uploaded to the channel Mike, the Mathematician 05 August 2024. Share the link to the video on social media so that your subscribers and friends will also watch this video. This video clip has been viewed 509 times and liked it 21 visitors.
