In finite dimension, $W_1^0+W_2^0=(W_1\cap W_2)^0$
14576
$(U\cap W)^0 = U^0 + W^0$
80892
Does $\wp(A \cap B) = \wp(A) \cap \wp(B)$ hold? How to prove it?
53633
Given two subspaces $U,W$ of vector space $V$, how to show that $\dim(U)+\dim(W)=\dim(U+W)+\dim(U\cap W)$
75863
how to prove $f^{-1}(B_1 \cap B_2) = f^{-1}(B_1) \cap f^{-1}(B_2)$
81471
Finite dimensional spaces
147888
Show that $M=\bigcap_{\mathfrak{p}\in\operatorname{Spec}(R)}M_\mathfrak{p}=\bigcap_{\mathfrak{m}\in\text{Max}(R)}M_\mathfrak{m}$ for certain $M$.
83713
If $z,w\in \mathbb{C}^{\times}$, then $|z+w|=|z|+|w|$ iff $w=tz$ for some $t\gt 0$
6366
Combinatorial proof of summation of $\sum\limits_{k = 0}^n {n \choose k}^2= {2n \choose n}$
64500
$\aleph_1 = 2^{\aleph_0}$
74623
Associative rule of subspaces and vector spaces: $(U+V) \cap W = U + (V \cap W)$
13572
$x^y+y^x>1$ for all $(x, y)\in \mathbb{R_+^2}$
54380
Prove if $|z| < 1$ and $ |w| < 1$, then $|1-zw^*| \neq 0$ and $| {{z-w} \over {1-zw^*}}| < 1$
106408
Prove that if W is a subspace of a finite dimensional vector space V, then dim(W) ≤ dim(V).
53364
dim$(V)$ = $n$, dim$(W)$ = $m$ $\implies$ dim($L(V,W)$) = $nm$
85239
Proof $dim(W)=dim(V)=n \implies W=V$
28781
$k^{2}+(k+1)^{2}$ being a perfect square for infinitely many $k$
23071
Showing that $f_0 (x_1, \ldots, x_m) \mathrm tr A =\displaystyle{ \sum_{i=1}^n} f_0(x_1, \ldots, Ax_i,\ldots, x_m)$