If I have a product of matrices of rank 1, the product is not going to have rank greater than 1. why?
2026-03-30 03:20:34.1774840834
Rank of matrix products is never greater than what
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Consider two matrices $A,B$ with rank one. Then the image of $B$ has rank one. Now $A$ (when you do the product $AB$) can be considered as acting on an $1$-dimensional subspace. So its image has at most rank one.