prove that if W is a subspace of V, then dim(W)+dim(W^0)=dim(V)
121047
Proof: Sum of dimension of orthogonal complement and vector subspace
125184
Why $\dim(\hom(V,W))=\dim(V) * \dim(W)$?
14576
$(U\cap W)^0 = U^0 + W^0$
65162
Show that $\dim H^0(\mathbb{P}^n, \mathcal{O}_{\mathbb{P}^n}(m)) = {n + m \choose n}$ if $m \geq 0$, and $0$ otherwise.
138212
Please help me prove: $v(a+b)\leq v(a)+v(b)$, and $v(ab)\leq v(a)v(b)$ where $v(x)=\inf{\{\vert x^n \vert}^{1/n}: n\in\mathbb{N}\}$
14429
dimension of a subspace spanned by two subspaces
4319
Vector space can be written as direct sum of subspaces
92291
$U_1, U_2, ..., U_k$ subspaces of linear space $X$ with same dimensions, prove $X=U_1\oplus V=U_2\oplus V=...=U_k\oplus V$
95379
Prove that $V = V_1 \oplus V_2$ in the following
79061
show that {$(x_1,x_2,x_3,x_4)\in\mathbb{F}^4$:$x_3=5x_4+b$} is a subspace
68006
Find the dimensions of some kernel subspaces of $\operatorname{Hom}(V, W)$.
103380
Is $\operatorname{height} \mathfrak{p} + \dim A / \mathfrak{p} = \dim A$ true?
94929
Proof that the all bases of a subspace V consist of the same number of vectors?
53261
Show that Pn is an (n+1)-dimensional subspace
24585
Proving that $\mathbf{W}$+$\mathbf{W^{\perp}}$=$\mathbb{R^{n}}$
49296
Prove $|(1+|u|^2)v-(1+|v|^2)u|>|u\bar{v}-\bar{u}v|$
74623
Associative rule of subspaces and vector spaces: $(U+V) \cap W = U + (V \cap W)$