query: Rank of matrices, prove inequality
positive_passages.docid: 33451
positive_passages.text: Sylvester rank inequality: $\operatorname{rank} A + \operatorname{rank}B \leq \operatorname{rank} AB + n$
negative_passages.docid: 139692
negative_passages.text: Proof of inequality using AM-GM inequality
negative_passages.docid: 5369
negative_passages.text: Proving the inequality $|a-b| \leq |a-c| + |c-b|$ for real $a,b,c$
negative_passages.docid: 90964
negative_passages.text: Prove: symmetric positive definite matrix
negative_passages.docid: 27821
negative_passages.text: A problem on rank of $A$ and $\operatorname{adj}(A)$
negative_passages.docid: 29198
negative_passages.text: How to prove the following inequality $|\prod_{i=1}^{i=n}a_i-\prod_{i=1}^{i=n}b_i| < n\delta$?
negative_passages.docid: 123151
negative_passages.text: Find the rank of matrix.
negative_passages.docid: 106979
negative_passages.text: Prove the inequality and limitation
negative_passages.docid: 44383
negative_passages.text: Finding rank of a matrix depending on parameter a
negative_passages.docid: 4952
negative_passages.text: Let $A$ be a diagonalizable matrix and $\lambda$ be an eigenvalue of A. Prove that rank($\lambda I - A$) = rank(($\lambda I - A)^2$).
negative_passages.docid: 146847
negative_passages.text: Given a square matrix A of order n, prove $\operatorname{rank}(A^n) = \operatorname{rank}(A^{n+1})$
negative_passages.docid: 70528
negative_passages.text: Rank of a Matrix Sum
negative_passages.docid: 35897
negative_passages.text: Proof of: $AB=0 \Rightarrow Rank(A)+Rank(B) \leq n$
negative_passages.docid: 128990
negative_passages.text: Prove that, at least one of the matrices $A+B$ and $A-B$ has to be singular
negative_passages.docid: 30866
negative_passages.text: Relation between rank and number of distinct eigenvalues of a matrix
negative_passages.docid: 65168
negative_passages.text: Proof of sequence inequality
negative_passages.docid: 70711
negative_passages.text: Inequality between 2 norm and 1 norm of a matrix