query: Calculate $X_A(x) $ and $m_A(x) $ of a matrix $A\in \mathbb{C}^{n\times n}:a_{ij}=i\cdot j$
positive_passages.docid: 2271
positive_passages.text: Determinant of a rank $1$ update of a scalar matrix, or characteristic polynomial of a rank $1$ matrix
negative_passages.docid: 78224
negative_passages.text: Suppose $A$ is a general $n \times n$ matrix and $B$ is obtained by interchanging two rows of $A$. Prove that $\det(B) = -\det(A)$
negative_passages.docid: 149086
negative_passages.text: Determining $\mbox{tr}(A)$ and $\det(A)$ as functions of the eigenvalues of a matrix
negative_passages.docid: 122434
negative_passages.text: Adjoint of a matrix and inverse of a matrix
negative_passages.docid: 58491
negative_passages.text: Proving the inverse of a matrix as a polynomial of matrices
negative_passages.docid: 6960
negative_passages.text: Necessary and sufficient condition for the matrix $A = I - 2 x x^t$ to be orthogonal
negative_passages.docid: 107128
negative_passages.text: Let $B$ be a nilpotent $n\times n$ matrix with complex entries let $A = B-I$ then find $\det(A)$
negative_passages.docid: 123726
negative_passages.text: $2\times 2 $ matrices over $\mathbb{C}$ that satisfy $\mathrm A^3=\mathrm A$
negative_passages.docid: 145768
negative_passages.text: The inverse of a matrix in which the sum of each row is $1$
negative_passages.docid: 146243
negative_passages.text: Does there exist a matrix $\mathbf{A}\in\mathbb{R}^{3\times3}$ such that $\mathbf{A}^{2}=-\mathbf{I}$?
negative_passages.docid: 77554
negative_passages.text: Inverse of the sum of matrices
negative_passages.docid: 116824
negative_passages.text: Find the sum of two elements in a matrix
negative_passages.docid: 10083
negative_passages.text: Determinant of matrix times a constant.
negative_passages.docid: 60006
negative_passages.text: Matrix equation: $A−A(A + B)^{−1}A = B−B(A + B)^{−1}B$
negative_passages.docid: 20331
negative_passages.text: Determinant of a $2\times 2$ block matrix
negative_passages.docid: 88712
negative_passages.text: Determining a matrix from its characteristic polynomial
negative_passages.docid: 87441
negative_passages.text: Proof involving matrix equation