$W$ contains at least one non-singular matrix
2109
Max dimension of a subspace of singular $n\times n$ matrices
39334
Non-degenerate bilinear forms and invertible matrices
69542
Why do the $n \times n$ non-singular matrices form an "open" set?
146455
Compactness of the set of all unitary matrices in $M_2(\mathbb{C})$
88820
Three linked question on non-negative definite matrices.
47012
When a 0-1-matrix with exactly two 1’s on each column and on each row is non-degenerated? [1]
15300
How to show that $(W^\bot)^\bot=W$ (in a finite dimensional vector space)
1865
Sub-determinants of an orthogonal matrix
73677
If the matrix $A^3 = 0$, is $A$ singular?
108012
A matrix $M$ that commutes with any matrix is of the form $M=\alpha I$
97487
How to prove whether a matrix has rank $1$
40222
Matrices that are not diagonal or triangular, whose eigenvalues are the diagonal elements
19946
Let $W$ be a given subspace of $V$ find the orthogonal complement $W^{\perp}$
41520
Prove that $L(V,W)$ forms a vector space
1770
Matrix $M_1 = M(f', \mathcal{B}, \mathcal{B '})$ of $f$
54628
Properties of non-zero symmetric bilinear form
30268
Positive definite matrix must be Hermitian