V is a linear space of n dimensions, show that V has subspaces of every dimension between 0 and n.
124786
Prove that V contains a subspace of each dimension
13880
Example of vector space such that $cv = 0$ where $c \ne 0$ and $v \ne \vec{0}$
64156
Why an eigenspace is a linear subspace, if the zero vector is not an eigenvector?
153747
Sub-dimensional linear subspaces of $\mathbb{R}^{n}$ have measure zero.
125212
How to Show that the Only Subspaces of $R^2$ are the zero subspace, $R^2$ itself, and the lines through the origin
33642
Finite dimensional subspace of $C([0,1])$
94929
Proof that the all bases of a subspace V consist of the same number of vectors?
74764
Dimension for a closed subspace of $C[0,1]$.
117575
Every proper subspace of a normed vector space has empty interior
106487
Let $S$ and $W$ be subsets of a vector space $V$. Show that if $S$ is a subset of $W$, then $\mathrm{span}(S)$ is a subspace of $\mathrm{span}(W)$
107000
Dimension of intersection of distinct subspaces
98949
Subspaces and annihilators
53261
Show that Pn is an (n+1)-dimensional subspace
73690
If $\mathbb R^3\setminus V$ connected where $V$ is the subspace generated by $\{(1,1,1),(0,1,1)\} $
53633
Given two subspaces $U,W$ of vector space $V$, how to show that $\dim(U)+\dim(W)=\dim(U+W)+\dim(U\cap W)$
119782
Suppose $S_1 =\{ u_1 , u_2 \}$ and $S_2 = \{ v_1 , v_2 \}$ are each independent sets of vectors in an n-dimensional vector space V.
6547
Given $3$-dimensional subspaces $V, W \subset \Bbb R^5$, there is a nonzero vector in $V \cap W$