Does every linearly independent set of n vectors in $R^n$ forms a basis in $R^n$?
8291
If $n$ vectors are linearly independent, is their span $\mathbb{R}^n$?
97049
If $v_1,...,v_m$ are linearly independent, then the span $v_1+w,...,v_m+w$ has dimension $\ge m-1$
69497
Show that the set of all $n \times n$ orthogonal matrices, $O(n)$, is a compact subset of $\mbox{GL} (n,\mathbb R)$
48113
Find a basis for the vector space of symmetric matrices with an order of $n \times n$
62065
Prove that $v_1, \dots v_n$ is a basis of V.
42495
Determine if the following sets of vectors are linearly independent
43282
Why do $n$ linearly independent vectors span $\mathbb{R}^{n}$?
152147
Why is a set of orthonormal vectors linearly independent?
723
Is there a constructive way to exhibit a basis for $\mathbb{R}^\mathbb{N}$?
42883
Cross product in $\mathbb R^n$
128835
Compactness of the set of $n \times n$ orthogonal matrices
23372
Show that for an invertible matrix, the images of a set of vectors spanning the space also form a spanning set
112939
Find a basis for the subspace of $\mathbb{R}^4$ spanned by the given vectors.
92600
Let $V$ be a $K$-vector space, $f: V \rightarrow V$ a linear map. Under some condition, show that $v, f(v),...,f^n(v)$ are linearly independent.
72952
Uniqueness of a linear map on a basis of a vector space
107248
Prove that the set $ \{\sin(x),\cos(x),\sin(2x),\cos(2x)\}$ is linearly independent.
120535
Basis of the polynomial vector space