prove that $Span(A)$ is a subspace of $Span(B)$
7462
If X and Y are two sets of vectors in a vector space V, and if X $\subset$ Y, then is span X $\subset$ span Y?
4717
The union of linear subspaces is not necessarily a subspace
73773
$C(M)=\{A\in M_n(\mathbb{C}) \mid AM=MA\}$ is a subspace of dimension at least $n$.
93511
Prove that $C^1([a,b])$ with the $C^1$- norm is a Banach Space
150135
The intersection of an infinite number of subspaces is a subspace
84871
Determining the dimension of span$\{AB-BA : A,B \in M_{n \times n}(\mathbb R) \}$
91022
How do I prove that a subspace of a vector space $X$ is the null space of some linear functional on $X$?
90525
The subspace of $\ell_2$
14429
dimension of a subspace spanned by two subspaces
43504
Proving the existence of a complement subspace $U' \subset V$.
28391
Prove the compactness of a set B
118996
Prove that $T$ is an orthogonal projection
41013
Subspace of $C^3$ that spanned by a set over C and over R
13167
Prove $A = (A \setminus B) \cup (A \cap B)$
83054
Let $E$ be a Banach space, prove that the sum of two closed subspaces is closed if one is finite dimensional
57771
Let $A\in M_{n\times n}(\Bbb R)$ so that $I\notin span(A,A^2,...,A^n)$. Prove that $\det(A)=0$.
53633
Given two subspaces $U,W$ of vector space $V$, how to show that $\dim(U)+\dim(W)=\dim(U+W)+\dim(U\cap W)$