Existence of a nonsingular submatrix
64644
An $r\times r$ submatrix of independent rows and independent columns is invertible (Michael Artin's book).
129465
Minimizing Frobenius norm of a special type
62232
A real $2 \times 2 $ matrix $M$ such that $M^2 = \tiny \begin{pmatrix} -1&0 \\ 0&-1-\epsilon \\ \end{pmatrix}$ , then :
53863
Making a non-diagonalizable matrix diagonalizable with an small perturbations
150674
Uniqueness in existence of a bilinear form
58339
The diagonalizable matrices are not dense in the square real matrices
139087
polar decomposition of a square A when A is not full rank/invertible
66842
Number of $n^2\times n^2$ permutation matrices with a 1 in each $n\times n$ subgrid
19132
Similar matrices have the same eigenvalues with the same geometric multiplicity
73697
Let $A, B$ be $n\times n$ with $n\ge 2$ nonsingular matrices with real entries such that $A^{-1} + B^{-1} =(A+B)^{-1}$
11566
Similar matrices and minimal polynomial
39800
Existence of solution for a linear system mod 2
141173
Are there matrices such that $AB=I$ and $BA \neq I$
86826
Almost a Vandermonde matrix
141529
Proving existence of a minimum
46309
Prove that this graph is nonplanar
12955
Classification of $n\times n$ real matrices up to congruence