query: Inverse of a particular matrix: $A = D + aJ$, all entries of $J$ are equal to $1$
positive_passages.docid: 149292
positive_passages.text: Inverse of a diagonal matrix plus a constant
negative_passages.docid: 22666
negative_passages.text: Proving that if $A^n = 0$, then $I - A$ is invertible and $(I - A)^{-1} = I + A + \cdots + A^{n-1}$
negative_passages.docid: 119301
negative_passages.text: Is the following matrix invertible?
negative_passages.docid: 124149
negative_passages.text: Inverse of matrix with nonnegative entries
negative_passages.docid: 116136
negative_passages.text: Proof that the inverse of a square matrix is unique
negative_passages.docid: 75480
negative_passages.text: Matrix Identity $(I-G_1G_2)^{-1}G_1=G_1(I-G_2G_1)^{-1}$?
negative_passages.docid: 87425
negative_passages.text: Prove that if $A$ is a square matrix with integer entries and $\det(A) = \pm 1$, then $A^{-1}$ contains all integer entries.
negative_passages.docid: 110408
negative_passages.text: Solving for $A$ in $Ax = b$
negative_passages.docid: 125021
negative_passages.text: Inverse of an invertible upper triangular matrix of order 3
negative_passages.docid: 129564
negative_passages.text: Show that $A$ is an invertible matrix if $\left(A+I\right)^3=0$ and find $A^{-1}$
negative_passages.docid: 155272
negative_passages.text: Is a matrix with $1$s in the diagonal and off-diagonal entries with absolute value less than $1$ invertible?
negative_passages.docid: 7457
negative_passages.text: Prove that $J^+AJ$ has positive eigenvalues
negative_passages.docid: 134402
negative_passages.text: $\mathrm{rank}(A)+\mathrm{rank}(I-A)=n$ for $A$ idempotent matrix
negative_passages.docid: 52928
negative_passages.text: If $\mathrm{Tr}(A)=0$ then $T=R^{-1}AR$ has all entries on its main diagonal equal to $0$
negative_passages.docid: 85845
negative_passages.text: Matrix with zeros on diagonal and ones in other places is invertible
negative_passages.docid: 23847
negative_passages.text: Determinant of a matrix whose $(i,j)$th element is $|i-j|$?
negative_passages.docid: 97733
negative_passages.text: Can it be determined that the sum of the diagonal entries, of matrix A, equals the sum of eigenvalues of A