List questions from inner-products | MathQA

What is the interpretation of the 'angle' between functions? Since $\langle f(x), g(x) \rangle= |f||g| \cos \alpha(?)$can be viewed as a inner product

Published on 01 Jul 2023 - 7:46

For three vectors in any inner product space, prove the following inequality.

Published on 06 Jul 2023 - 15:48

Coupling bra-ket notation to the definition of Hilbert space

Published on 11 Apr 2026 - 16:42

Polarization identity for normed space satisfying Ptolemy's inequality

Published on 06 Jul 2023 - 18:23

Definition of Angle between Complex Vectors

Published on 08 Apr 2026 - 16:17

Taking Trace with Multiple Metrics

Published on 25 Mar 2026 - 12:47

Proving Operator Equaility with Polarization Identity

Published on 11 Apr 2026 - 2:36

A Lower Bound on a Vector Expression

Published on 11 Jul 2023 - 15:31

Prove that $||v||^2 ≥ \dfrac{1}{n}$ - alternative way

Published on 17 Jul 2023 - 14:53

What would be the sum of two dot products with a common vector?

Published on 17 Jul 2023 - 16:32

$T$ and $U$ self-adjoint on $V$, $T$ is positive definite. Prove $TU$ & $UT$ are diagonalizable linear operators that have only real eigenvalues.

Published on 26 Mar 2026 - 6:30

Proof of Cauchy shwarz inequality with multiple parts

Published on 20 Jul 2023 - 3:09

Are the limits of Euclidean spaces Hilbert spaces?

Published on 07 Apr 2026 - 20:47

Matrices of self-adjoint operators

Published on 26 Mar 2026 - 6:20

The Inner Product of a Hadamard Product

Published on 25 Mar 2026 - 23:38