List questions from inner-products

Published on 16 May 2020 - 18:51

157

Views

Prove that if $x,y$ are eigenvectors of the same eigenvalue, then $\langle x,y \rangle \neq 0$.

Published on 17 May 2020 - 23:46

21

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Inequality about two inner product?

Published on 30 Mar 2026 - 2:04

175

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Is a normalized cosine similarity a Bregman divergence?

Published on 26 Mar 2026 - 16:05

49

Views

Problem about inequality with symetric matrices and inner product

Published on 25 Mar 2026 - 17:37

865

Views

Distributive Property of Dot Products - Geometrically, but a different approach.

Published on 04 Apr 2026 - 5:19

44

Views

If $(\alpha_i,\alpha_j)=(\beta_i,\beta_j)$ for $0<i,j<n+1$, then ${\rm L}(\alpha_1, ..., \alpha_n)\cong {\rm L}(\beta_1, ..., \beta_n)$?

Published on 25 May 2020 - 22:55

461

Views

Can the proof about direct sum decomposition of the inner product space be generalize to infinitely dimension space

Published on 27 Mar 2026 - 13:48

260

Views

Prove an inner product space

Published on 27 May 2020 - 6:19

111

Views

Let $x$ be a non zero vector in the complex vector space $\mathbb C^n$ and $A=xx^H$.Find all the Eigenvalues and their Eigen spaces.

Published on 27 May 2020 - 19:41

57

Views

Prove or give a counterexample for semi positive defined matrices

Published on 26 Mar 2026 - 19:16

51

Views

Please define $\ell^2$ space and give some examples of its subspaces

Published on 06 Apr 2026 - 10:42

121

Views

On Cauchy-Schwarz inequality

Published on 30 Mar 2026 - 3:53

69

Views

Orthogonal projection in a inner product space

Published on 28 May 2020 - 13:40

74

Views

Inner Product-Norm Inequality

Published on 25 Mar 2026 - 8:07

List Question

Prove dot product of sequences is equal to dot product of their limits

Prove that if $x,y$ are eigenvectors of the same eigenvalue, then $\langle x,y \rangle \neq 0$.

Inequality about two inner product?

Is a normalized cosine similarity a Bregman divergence?

Problem about inequality with symetric matrices and inner product

Distributive Property of Dot Products - Geometrically, but a different approach.

If $(\alpha_i,\alpha_j)=(\beta_i,\beta_j)$ for $0<i,j<n+1$, then ${\rm L}(\alpha_1, ..., \alpha_n)\cong {\rm L}(\beta_1, ..., \beta_n)$?

Can the proof about direct sum decomposition of the inner product space be generalize to infinitely dimension space

Prove an inner product space

Let $x$ be a non zero vector in the complex vector space $\mathbb C^n$ and $A=xx^H$.Find all the Eigenvalues and their Eigen spaces.

Prove or give a counterexample for semi positive defined matrices

Please define $\ell^2$ space and give some examples of its subspaces

On Cauchy-Schwarz inequality

Orthogonal projection in a inner product space

Inner Product-Norm Inequality

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