List questions from normed-spaces

Published on 12 Apr 2026 - 8:39

262

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Show that the norm is continuous in the following sense:

Published on 12 Apr 2026 - 13:37

204

Views

Does there exist an infinite dimensional real normed linear space which can be written as a countable union of one dimensional subspaces?

Published on 13 Apr 2026 - 1:54

725

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Showing that if $\inf_{\lambda\in\mathbb{R}}\| I - \lambda A\| < 1 $ then A is invertible

Published on 11 Apr 2026 - 9:34

495

Views

Using the fact that $X$ is isomorphic to $\mathbb{R}^n$ to prove that the unit sphere is compact in $X$.

Published on 16 Apr 2026 - 4:46

946

Views

Minimize frobenius norm of Gram matrix

Published on 14 Apr 2026 - 22:18

102

Views

Inequality in normed space with normalization

Published on 12 Apr 2026 - 6:49

98

Views

Questions on the subset of Test function space

Published on 10 Apr 2026 - 16:13

72

Views

Finding the greatest lower bounds on $||A||, ||A^-1||$ and $\kappa (A)$

Published on 11 Apr 2026 - 6:35

841

Views

Functional Analysis - Dual Space and finite dimensional normed vector spaces

Published on 12 Apr 2026 - 14:36

54

Views

How to derivate norms?

Published on 11 Apr 2026 - 5:01

1.1k

Views

Condition number of matrix multiplied with permutation matrix

Published on 11 Apr 2026 - 12:15

88

Views

How to prove $\||A|\|_2 \le \sqrt{n} \|A \|_2$?

Published on 11 Apr 2026 - 23:53

675

Views

Convergence of vectors in a normed vector space.

Published on 16 Apr 2026 - 12:29

73

Views

Utility of standard matrix norm

Published on 14 Apr 2026 - 11:07

List Question

Inner Product: Proof Of Second & Third Axiom for Normed Linear Space

Show that the norm is continuous in the following sense:

Does there exist an infinite dimensional real normed linear space which can be written as a countable union of one dimensional subspaces?

Showing that if $\inf_{\lambda\in\mathbb{R}}\| I - \lambda A\| < 1 $ then A is invertible

Using the fact that $X$ is isomorphic to $\mathbb{R}^n$ to prove that the unit sphere is compact in $X$.

Minimize frobenius norm of Gram matrix

Inequality in normed space with normalization

Questions on the subset of Test function space

Finding the greatest lower bounds on $||A||, ||A^-1||$ and $\kappa (A)$

Functional Analysis - Dual Space and finite dimensional normed vector spaces

How to derivate norms?

Condition number of matrix multiplied with permutation matrix

How to prove $\||A|\|_2 \le \sqrt{n} \|A \|_2$?

Convergence of vectors in a normed vector space.

Utility of standard matrix norm

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