query: Rank of matrix products is never greater than what
positive_passages.docid: 41026
positive_passages.text: How to prove and interpret $\operatorname{rank}(AB) \leq \operatorname{min}(\operatorname{rank}(A), \operatorname{rank}(B))$?
negative_passages.docid: 65783
negative_passages.text: Proving: "The trace of an idempotent matrix equals the rank of the matrix"
negative_passages.docid: 158343
negative_passages.text: how to prove an element is non-zero in a tensor-product
negative_passages.docid: 87494
negative_passages.text: $\operatorname{rank}(T^3) + \operatorname{rank}(T) \geq 2\operatorname{rank}(T^2)$ for finite-dimensional $V$
negative_passages.docid: 137093
negative_passages.text: What is the codimension of matrices of rank $r$ as a manifold?
negative_passages.docid: 145535
negative_passages.text: Product norm on infinite product space
negative_passages.docid: 87636
negative_passages.text: A Product function for matrix products
negative_passages.docid: 121157
negative_passages.text: Proof verification: column rank = row rank
negative_passages.docid: 1751
negative_passages.text: When does the tensor product distribute over an infinite direct product?
negative_passages.docid: 145161
negative_passages.text: Testing whether an element of a tensor product of modules is zero
negative_passages.docid: 122853
negative_passages.text: Show that $\operatorname{rank}(A) = \operatorname{rank}(B)$
negative_passages.docid: 47589
negative_passages.text: Product of a primitive matrix and its transpose.
negative_passages.docid: 898
negative_passages.text: Strictly diagonally dominant matrices are non singular
negative_passages.docid: 152869
negative_passages.text: Rank of circulant matrix with $k$ ones per row
negative_passages.docid: 62283
negative_passages.text: How can I quickly know the rank of this / any other matrix?
negative_passages.docid: 105405
negative_passages.text: Product of three consecutive positive integers is never a perfect power
negative_passages.docid: 33451
negative_passages.text: Sylvester rank inequality: $\operatorname{rank} A + \operatorname{rank}B \leq \operatorname{rank} AB + n$