query: Rank of the sum of an all-ones matrix and an identity matrix
positive_passages.docid: 21758
positive_passages.text: Rank of the $n \times n$ matrix with ones on the main diagonal and $a$ off the main diagonal
negative_passages.docid: 123483
negative_passages.text: Prove that $\operatorname{rank}(A) + \operatorname{rank}(B) \ge \operatorname{rank}(A + B)$
negative_passages.docid: 26570
negative_passages.text: Prove $\operatorname{rank}(AB) = \operatorname{rank}(B)$
negative_passages.docid: 4205
negative_passages.text: Is adjoint of singular matrix singular? What would be its rank?
negative_passages.docid: 84279
negative_passages.text: The average determinant of all integer matrices with coefficients $0,1,2$
negative_passages.docid: 2798
negative_passages.text: A and B are nxn matrices, $A =B^TB$. Prove that if rank(B)=n, A is pos def, and if rank(B)<b, A is pos semi-def.
negative_passages.docid: 46128
negative_passages.text: Representation of Matrix with Rank 1
negative_passages.docid: 10483
negative_passages.text: Prove Sylvester rank inequality: $\text{rank}(AB)\ge\text{rank}(A)+\text{rank}(B)-n$
negative_passages.docid: 97487
negative_passages.text: How to prove whether a matrix has rank $1$
negative_passages.docid: 98631
negative_passages.text: Postive-semidefiniteness of matrix with entries $1/(a_i+a_j)$
negative_passages.docid: 82688
negative_passages.text: Least rank of a matrix
negative_passages.docid: 67058
negative_passages.text: Prove that $\text{rank}(X^TX)=\text{rank}(X)$
negative_passages.docid: 73297
negative_passages.text: Two idempotent matrices are similar iff they have the same rank
negative_passages.docid: 76160
negative_passages.text: Dimension of the sum of two vector subspaces
negative_passages.docid: 121157
negative_passages.text: Proof verification: column rank = row rank
negative_passages.docid: 76335
negative_passages.text: Proving that two matrices are congruent, in order to establish a rank and signature result.
negative_passages.docid: 45532
negative_passages.text: Let $A$ be a $n\times n$ matrix with entries $a_{ij}=i+j $ . Calculate rank of $A$