query: Prove that If A is a real skew-symmetric matrix, then I + A is invertible, where I is the identity matrix.
positive_passages.docid: 18585
positive_passages.text: Showing $A-I$ is invertible, when $A$ is a skew-symmetric matrix
negative_passages.docid: 133036
negative_passages.text: Jordan normal form and invertible matrix of generalized eigenvectors proof
negative_passages.docid: 64742
negative_passages.text: Prove a residue matrix $A$ (with coefficients in $\mathbb Z_n)$ has an inverse if and only if $\gcd(\det A,n) = 1$
negative_passages.docid: 148946
negative_passages.text: If $\mathbf{A}$ is a $2\times 2$ matrix that satisfies $\mathbf{A}^2 - 4\mathbf{A} - 7\mathbf{I} = \mathbf{0}$, then $\mathbf{A}$ is invertible
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: 75215
negative_passages.text: Properties of invertible matrices
negative_passages.docid: 13026
negative_passages.text: Prove that if AB=I_m, then rk(A)=rk(B).
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: 153119
negative_passages.text: $x^TAx=0$ for all $x$ when $A$ is a skew symmetric matrix
negative_passages.docid: 33448
negative_passages.text: Proof if $AB+BA=0$ Then atleast one of the matrices are singular.
negative_passages.docid: 69980
negative_passages.text: Proving that if $A$ is an $n\times n$ orthogonal matrix, then $\det(A) = \pm1$
negative_passages.docid: 65783
negative_passages.text: Proving: "The trace of an idempotent matrix equals the rank of the matrix"
negative_passages.docid: 142640
negative_passages.text: Prove determinant of a matrix $=\prod_{j<i}(a_i-a_j)$
negative_passages.docid: 70455
negative_passages.text: Why are all nonzero eigenvalues of the skew-symmetric real matrices pure imaginary?
negative_passages.docid: 20920
negative_passages.text: Determinant of a block skew-symmetric matrix
negative_passages.docid: 73155
negative_passages.text: Prove that for any square matrix, an invertible matrix B exists, so that BA is triangular
negative_passages.docid: 118304
negative_passages.text: If $A^2 = I$ (Identity Matrix) then $A = \pm I$