Cauchy-Schwarz on real vector space: $| \langle u, v \rangle | = \| u \| \cdot \| v \| \iff u =\frac {\langle u, v \rangle} {\langle v, v \rangle} v$
33637
Proofs of the Cauchy-Schwarz Inequality?
10907
Necessity of completeness of the inner product space in Riesz representation theorem
5506
Perturbation property of Orthonormal basis for Hilbert space
43504
Proving the existence of a complement subspace $U' \subset V$.
41069
Justifying $\,\Bbb{Z}[i]/\langle 2\rangle\cong \Bbb{Z}[X]/\langle X^2+1,2\rangle\cong \Bbb{F}_2[X]/\langle X^2+1\rangle$
149634
$ 2|f^{'}(0)| = \sup_{z, w \in D} |f(z)-f(w)|$
30996
If $\langle Ta, a\rangle \in \mathbb{R}$ for all $a$ then $T$ is self-adjoint
102871
$\langle r\rangle$ maximal $\iff r$ irreducible
128985
Show that $\langle x,y\rangle_A = \langle Ax,Ay\rangle$ is an inner product on $\mathbb R^n$
97391
Prove that $(C^1[0,1], \|\cdot\|)$ is not a Banach space
119352
compact and self adjoint square root of an operator
27086
proof for $\langle q| p \rangle = e^{ipq}$
36319
Intuition on proof of Cauchy Schwarz inequality
70475
Proving a basis for inner product space V when $||e_j-v_j||< \frac{1}{\sqrt{n}}$.
44685
Inner product on $C(\mathbb R)$
93910
Equality in Cauchy-Schwarz Inequality implies linear dependence.
95030
Proving the Cauchy-Schwarz inequality by induction