If the columns of an $n \times n$ matrix are linearly independent, then the columns span $\mathbb{R}^{n}$
43282
Why do $n$ linearly independent vectors span $\mathbb{R}^{n}$?
31149
Prove that matrix can be square of matrix with real entries
40409
If a subspace S is spanned by $n$ vectors, any subset of S with $m>n$ vectors is linearly dependent
34372
Are $10\times 10$ matrices spanned by powers of a single matrix?
27474
A square matrix $n \times n$ is an invertible matrix iff the rank of the matrix is $n$.
94077
Proof of linear independence of $e^{at}$
42046
How to tell if a set of vectors spans a space?
50159
How to prove if $\Bbb R^n=W_1\cup W_2\cup \cdots\cup $ where each $W_k$ is a subspace, then $\Bbb R^n=W_i$ holds for some $i$
42883
Cross product in $\mathbb R^n$
36878
Prove that $\operatorname{SL}(n,\Bbb R)$ is connected.
115954
how to find maximal linearly independent subsets
55752
Prove that $n+1$ vectors in $\mathbb{R}^n$ cannot be linearly independent
140711
Linear independence of images by $A$ of vectors whose span trivially intersects $\ker(A)$
994
Linear independence of vectors that form non-square matrix
86749
Prove that any set of vectors $S \subset \mathbb{R}^n$ containing the zero vector cannot be linearly independent
72567
Does a set of $n$ independent vectors in $R^{n}$ always span $R^{n}$?
107641
Show that an infinite set of families are linearly independent