Are vectors $e_i$ linearly independent if and only if the matrix $A$ is nonsingular?
19846
Gram matrix invertible iff set of vectors linearly independent
119032
Is ${\bf x^TAx} \ge { a \bf x^Tx}$ for some $a>0$ not dependent on $\bf x$ if $\bf A$ is positive definite matrix?
9250
Can the zero vector be an eigenvector for a matrix?
62058
How to prove $1$,$\sqrt{2},\sqrt{3}$ and $\sqrt{6}$ are linearly independent over $\mathbb{Q}$?
20728
Proof that this is independent
31116
Matrix given by $a_{ij} = 1/(i+j)$ is non-singular.
43282
Why do $n$ linearly independent vectors span $\mathbb{R}^{n}$?
57626
Are Jordan chains always linearly independent?
61281
Finding maximal sublist of linearly independent vectors
118867
Independence of Gaussian variables
100656
$2\times2$ matrix $A$ such that $A$ has one independent eigenvector while $A^{2}$ has two independent eigenvectors
75215
Properties of invertible matrices
108012
A matrix $M$ that commutes with any matrix is of the form $M=\alpha I$
132492
If a linear transformation $T$ has $z^n$ as the minimal polynomial, there is a vector $v$ such that $v, Tv,\dots, T^{n-1}v$ are linearly independent
152147
Why is a set of orthonormal vectors linearly independent?
135316
A basic question on diagonalizability of a matrix
126769
Linear independence of columns implies non-zero determinant