non-singular matrix. Show if $a^TAa \neq -1$
53899
Proof of the Sherman-Morrison Formula
101861
How do you prove that $tr(B^{T} A )$ is a inner product?
30923
Is the matrix $A^*A$ and $AA^*$ hermitian?
87441
Proof involving matrix equation
118417
Is $AA^T$ positive semidefinite?
43570
Finding two non-zero matrices where $AX = BA$
40517
Determinant of a non-square matrix
131701
Why is $A^TA$ invertible if $A$ has independent columns?
143793
If $A$ is symmetric, then the matrix exponential $e^{A}$ is positive definite
149219
If $A$ is a non-square matrix with orthonormal columns, what is $A^+$?
89729
If $X$ is a singular matrix, then is $X'X$ singular?
132366
Diagonalizability of $A \in M_{n}(\Bbb{R})$ (Upper traingular matrix) with all diagonal entries 1 and $A \neq I$?
50384
A matrix and its transpose have the same set of eigenvalues/other version: $A$ and $A^T$ have the same spectrum
7457
Prove that $J^+AJ$ has positive eigenvalues
57543
Show that a matrix is nilpotent.
55031
Show any matrix $A_{n\times n}$ can be written as sum of two nonsingular matrices
124095
$A$ is a real orthogonal matrix, prove that $ (I+A)^{-1}(I-A)$ is skew-symmetric