Question

Where does this proof that the abs. value of the determinant of a 2x2 matrix A is the area of the image of the unit square under A go wrong?

score 805 · Answer 1 · 2026-04-15 01:07:48

805

Views

Where does this proof that the abs. value of the determinant of a 2x2 matrix A is the area of the image of the unit square under A go wrong?

Published on 15 Apr 2026 - 1:07

score 305 · Answer 2 · 2026-04-14 08:51:16

305

Views

Are the $||x||_p$ norms dense in the set of all norms of $\mathbb{R}^n$?

Published on 14 Apr 2026 - 8:51

score 462 · Answer 3 · 2026-04-10 06:14:23

462

Views

An inequality between determinant and norm.

Published on 10 Apr 2026 - 6:14

score 2.5k · Answer 4 · 2026-04-14 16:52:01

2.5k

Views

Show that $1/(1+\|A\|) < \|(I-A)^{-1}\| <1/(1-\|A\|)$

Published on 14 Apr 2026 - 16:52

score 57 · Answer 5 · 2026-04-14 11:27:04

57

Views

Why does $X$ not Banach $\implies x\mapsto \bar x$ is not onto?

Published on 14 Apr 2026 - 11:27

score 242 · Answer 6 · 2026-04-13 11:01:49

242

Views

Mazur–Ulam Theorem - Why is Isometry of Normed Vector Spaces over R only Affine and not Linear?

Published on 13 Apr 2026 - 11:01

score 315 · Answer 7 · 2026-04-16 10:47:01

315

Views

If $Y$ is complete show that $T_nx\to T(x) ;T\in B(X,Y)$

Published on 16 Apr 2026 - 10:47

score 237 · Answer 8 · 2026-04-14 09:56:55

237

Views

Show that $(||x_n||)$ is bounded.

Published on 14 Apr 2026 - 9:56

score 1.1k · Answer 9 · 2026-04-16 05:42:00

1.1k

Views

Prove that the norm of an integrable vector function is integrable

Published on 16 Apr 2026 - 5:42

score 1.2k · Answer 10 · 2026-04-10 20:25:03

1.2k

Views

Show that if a linear operator between Banach spaces is not onto, then its image is a meager set

Published on 10 Apr 2026 - 20:25

score 26 · Answer 11 · 2026-04-11 15:55:18

26

Views

Transformation of $L^2$ norm to another interval (failing in exercise)

Published on 11 Apr 2026 - 15:55

score 36 · Answer 12 · 2026-04-11 04:40:39

36

Views

Structures induced from other structures

Published on 11 Apr 2026 - 4:40

score 124 · Answer 13 · 2026-04-14 14:42:00

124

Views

Finding a convex set that approaches a boundary point

Published on 14 Apr 2026 - 14:42

score 64 · Answer 14 · 2026-04-15 18:49:12

64

Views

If $f: \mathbb{R}^{n} \mapsto \mathbb{R}$, can we replace $||Df||$ by $||\nabla f ||$?

Published on 15 Apr 2026 - 18:49

score 33 · Answer 15 · 2026-04-16 21:13:32

33

Views

Show that $N_p^p (f+g) \le N_p^p(f) + N_p^p (g)$ for $p\in ]0,1]$

Published on 16 Apr 2026 - 21:13

List Question

Where does this proof that the abs. value of the determinant of a 2x2 matrix A is the area of the image of the unit square under A go wrong?

Are the $||x||_p$ norms dense in the set of all norms of $\mathbb{R}^n$?

An inequality between determinant and norm.

Show that $1/(1+\|A\|) < \|(I-A)^{-1}\| <1/(1-\|A\|)$

Why does $X$ not Banach $\implies x\mapsto \bar x$ is not onto?

Mazur–Ulam Theorem - Why is Isometry of Normed Vector Spaces over R only Affine and not Linear?

If $Y$ is complete show that $T_nx\to T(x) ;T\in B(X,Y)$

Show that $(||x_n||)$ is bounded.

Prove that the norm of an integrable vector function is integrable

Show that if a linear operator between Banach spaces is not onto, then its image is a meager set

Transformation of $L^2$ norm to another interval (failing in exercise)

Structures induced from other structures

Finding a convex set that approaches a boundary point

If $f: \mathbb{R}^{n} \mapsto \mathbb{R}$, can we replace $||Df||$ by $||\nabla f ||$?

Show that $N_p^p (f+g) \le N_p^p(f) + N_p^p (g)$ for $p\in ]0,1]$

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