query: $A$ is an invertible matrix such that the sum of each row is $1$
positive_passages.docid: 145768
positive_passages.text: The inverse of a matrix in which the sum of each row is $1$
negative_passages.docid: 64644
negative_passages.text: An $r\times r$ submatrix of independent rows and independent columns is invertible (Michael Artin's book).
negative_passages.docid: 28861
negative_passages.text: Given an invertible matrix $A$ such that all elements in $A$ and in $𝐴^{−1}$ are integers, find $|𝐴^4|$
negative_passages.docid: 82925
negative_passages.text: Let the matrix $A=[a_{ij}]_{n×n}$ be defined by $a_{ij}=\gcd(i,j )$. How prove that $A$ is invertible, and compute $\det(A)$?
negative_passages.docid: 133036
negative_passages.text: Jordan normal form and invertible matrix of generalized eigenvectors proof
negative_passages.docid: 51967
negative_passages.text: Prove that if the sum of each row of $A$ equals $s$, then $s$ is an eigenvalue of $A$.
negative_passages.docid: 121982
negative_passages.text: Show matrix A is invertible if and only if $a_0 \neq 0$ with $A^n+a_{n-1}A^{n-1}+....+a_1A+a_0I=O$.
negative_passages.docid: 55031
negative_passages.text: Show any matrix $A_{n\times n}$ can be written as sum of two nonsingular matrices
negative_passages.docid: 65305
negative_passages.text: Minimal polynomial for an invertible matrix and its determinant
negative_passages.docid: 85845
negative_passages.text: Matrix with zeros on diagonal and ones in other places is invertible
negative_passages.docid: 60598
negative_passages.text: Matrix $A^T A$ as sum of outer products
negative_passages.docid: 27474
negative_passages.text: A square matrix $n \times n$ is an invertible matrix iff the rank of the matrix is $n$.
negative_passages.docid: 139951
negative_passages.text: Direct Sum of vector subspaces
negative_passages.docid: 52564
negative_passages.text: $m\times n$ matrix with an even number of 1s in each row and column
negative_passages.docid: 108012
negative_passages.text: A matrix $M$ that commutes with any matrix is of the form $M=\alpha I$
negative_passages.docid: 51800
negative_passages.text: We have matrix $A\in M_{n-1\times n}(\mathbb Z)$ so that the sum of entries in each row is zero. Prove that $\det(AA^T)=nk^2.$
negative_passages.docid: 88473
negative_passages.text: Proof that the trace of a matrix is the sum of its eigenvalues