Prove that $Au\cdot v = u\cdot A^Tv$ with standard inner product
131609
Prove that $Au\cdot v = u\cdot A^Tv$
90332
Prove that that $U(n)$ is an abelian group.
62342
$x_1 \cdot \dots \cdot x_n=1 \implies x_1 + \dots + x_n \ge n$
152932
Proof: $\det\pmatrix{\langle v_i , v_j \rangle}\neq0$ $\iff \{v_1,\dots,v_n\}~\text{l.i.}$
44912
Prove that $ \overline {A^\complement} = (A°)^\complement $
142229
Prove that if $V \cap \text{Span}\{u_1, u_2,...,u_k\} = \{ 0\} $, then $Au_1, Au_2,...,Au_k$ are linearly independent
124786
Prove that V contains a subspace of each dimension
94383
Prove that $A^TD-C^TB=I$
126672
Product of principal ideals: $(a)\cdot (b) = (a b)$
120010
Show that $\aleph_{\alpha}^{\aleph_{1}} = \aleph_{\alpha}^{\aleph_{0}}\cdot 2^{\aleph_1}$
94077
Proof of linear independence of $e^{at}$
78191
Define $\|\cdot\| \colon V \rightarrow \mathbb{R} $ by $\|a\| =\sum 2^n |a_n| $, then choose the correct option
61666
Proving $ [(\vec{a}+\vec{b})\times(\vec{b}+\vec{c})]\cdot(\vec{c}+\vec{a})=2\vec{c}\cdot(\vec{b}\times\vec{a})$
15300
How to show that $(W^\bot)^\bot=W$ (in a finite dimensional vector space)
121047
Proof: Sum of dimension of orthogonal complement and vector subspace
95806
Proving commutativity of convolution $(f \ast g)(x) = (g \ast f)(x)$
27901
Proving $\sum\limits_{i=1}^k | \langle x,v_i \rangle \langle y,v_i\rangle| \leq \|x\|\cdot \|y\|$