prove sum of inner products of v and an orthonormal set is smaller than v
127047
How to show that $\sum_{i=1}^n | \langle f, f_i\rangle |^2 \leq \Vert f \Vert^2$
158852
If $\{v_1, v_2, v_3\}$ is an orthonormal basis of $\mathbb{R}^3$ and $v = a_1v_1 + a_2v_2 + a_3v_3$, can we have $|a_1| > 3$?
78648
Find an orthonormal basis for the subspace of $\mathbb R^4$
77510
$\sum_{1}^{n}\left ( a_{i}b_{i} \right )\geq \prod_{1}^{n}\left ( a_{i}^{b_{i}} \right )$
118471
Prove that $1-\sum_{i=1}^n a_i < \prod_{i=1}^n(1-a_i) $
152196
About inner products, norms and metrics
44281
Proof of sum of kernels of concatenated vector
18839
Proof about inner product space $\vert \langle x,y\rangle \vert=\Vert x \Vert\Vert y \Vert$
88153
Finding all inner products on $\mathbb{R}^2$ for which a given linear map is orthogonal
43504
Proving the existence of a complement subspace $U' \subset V$.
20309
Product and sum of positive operators is positive
117688
Prove that $\def\Aut{\operatorname{Aut}}\Aut(\mathbf{Z_{n}})\simeq \mathbf{Z_{n}^{*}}$
44685
Inner product on $C(\mathbb R)$
149664
Norm is sup of inner products (proof).
5506
Perturbation property of Orthonormal basis for Hilbert space
27564
Prove that $\|UVU^{-1}V^{-1}-I\|\leq 2\|U-I\|\|V-I\|$
73952
Upper bound for the sum of absolute values of the eigenvalues