Find basis and dimension for $V$
87692
Basis and dimension of vector space
59192
Basis of cotangent space
21155
Finding basis of $\mathbb{Q}(\sqrt{2},\sqrt{3},\sqrt{5})$ over $\mathbb{Q}$
107122
Compute $ad_X$, $ad_Y$, and $ad_Z$ relative to a basis
154724
Every vector space has a basis
145094
Is my basis for $U=\{p \in \mathcal P_4(\mathbb R) \mid p(6)=0\}$ correct?
12698
Orthonormal basis for $\mathcal{L}^2([0,1])$
41347
The dimension of the intersection of two vector subspaces
142097
Finding the dimension of the orthogonal complement
68552
Find the representing matrix with the respect to the standard basis
88728
Dimensions of vector subspaces in a direct sum are additive
76160
Dimension of the sum of two vector subspaces
15811
Finding a basis for a certain vector space of periodic polynomials
115273
Nilpotent matrix and basis for $F^n$
106408
Prove that if W is a subspace of a finite dimensional vector space V, then dim(W) ≤ dim(V).
94929
Proof that the all bases of a subspace V consist of the same number of vectors?
24072
Intuitive explanation of why $\dim\operatorname{Im} T + \dim\operatorname{Ker} T = \dim V$