Yahoo Answers is shutting down on May 4th, 2021 (Eastern Time) and beginning April 20th, 2021 (Eastern Time) the Yahoo Answers website will be in read-only mode. There will be no changes to other Yahoo properties or services, or your Yahoo account. You can find more information about the Yahoo Answers shutdown and how to download your data on this help page.
Trending News
The rank of matrices (a Linear Algebra inequality)?
How would I go about showing that for two matrices A, B, that the rank of (AB) (i.e. the rank of the matrix product of A and B) is less than or equal to the minimum of the rank of A and the rank of B?
That is:
rank (AB) ≤ min (rank(A), rank(B))
Thanks so much! :)
1 Answer
- Michael TLv 51 decade agoFavorite Answer
I would start by exploring the issue for matrices in row-echelon form and see what you come up with. It makes sense it would be ≤ to the min since multiplying two matrices can't create new independent vectors and thus cannot increase the rank of the matrix you start with. What is more interesting is finding examples where this inequality is strict.
