query: Prove that if A is a square matrix with linearly indep columns, then $A^+$ = $A^{-1}$
positive_passages.docid: 149219
positive_passages.text: If $A$ is a non-square matrix with orthonormal columns, what is $A^+$?
negative_passages.docid: 137920
negative_passages.text: Proving an equation with invertible matrices
negative_passages.docid: 31898
negative_passages.text: Sufficient conditions for $x, Ax, A^2x, ...$ being linearly indepedent
negative_passages.docid: 64517
negative_passages.text: Prove that row rank of a matrix equals column rank
negative_passages.docid: 118283
negative_passages.text: Show that if $A^{n}=I$ then $A$ is diagonalizable.
negative_passages.docid: 32487
negative_passages.text: Proving $\det \left( \begin{smallmatrix} A & -B \\ B & A \end{smallmatrix} \right) =|\det(A+iB)|^2$
negative_passages.docid: 88746
negative_passages.text: Positive definiteness of the matrix $A+B$
negative_passages.docid: 29462
negative_passages.text: Suggestions on how to prove the following equality. $a^{m+n}=a^m a^n$
negative_passages.docid: 43913
negative_passages.text: Prove that if $A^*+A=AA^*$ then $A$ is normal
negative_passages.docid: 74341
negative_passages.text: Proving an invertible matrix which is its own inverse has determinant $1$ or $-1$
negative_passages.docid: 131212
negative_passages.text: Prove that if $A$ is regular then $\operatorname{adj}(\operatorname{adj}(A)) = (\det A)^{n-2} A$
negative_passages.docid: 110826
negative_passages.text: prove that : $ i = \sqrt {-1}\ $
negative_passages.docid: 147014
negative_passages.text: Matrix algebra: If $A^2=0$, Proof rank(A) $\le \frac{n}{2}$
negative_passages.docid: 97487
negative_passages.text: How to prove whether a matrix has rank $1$
negative_passages.docid: 78736
negative_passages.text: Check my proof that $(ab)^{-1} = b^{-1} a^{-1}$
negative_passages.docid: 154327
negative_passages.text: $A^2X = X$ show that $AX = X$, if $A_{ij} > 0$ and $x_{i} > 0$
negative_passages.docid: 81775
negative_passages.text: Prove $a^\alpha b^{1-\alpha} \le \alpha a + (1 - \alpha)b, \; a,b > 0,\; 0 < \alpha < 1$