Question

Every two norms on a finite dimensional (real or complex) vector space $V$ are equivalent.

score 632 · Answer 1 · 2026-04-09 08:06:51

632

Views

Every two norms on a finite dimensional (real or complex) vector space $V$ are equivalent.

Published on 09 Apr 2026 - 8:06

score 1.2k · Answer 2 · 2026-04-29 12:57:45

1.2k

Views

Consider the bisection method starting with the interval $[1.5, 3.5]$

Published on 29 Apr 2026 - 12:57

score 1k · Answer 3 · 2026-04-16 06:05:20

1k

Views

Show that $(a,b)\times (c,d)$ is an open set in $\mathbb{R}^2$ with the Euclidian metric.

Published on 16 Apr 2026 - 6:05

score 482 · Answer 4 · 2026-04-11 17:59:57

482

Views

Let $T: V \to W$ be a linear map. Let $V$ be finite dimensional. Then $T$ is continuous.

Published on 11 Apr 2026 - 17:59

score 65 · Answer 5 · 2026-04-16 23:56:46

65

Views

If $\sin c_n= 3c_n-a_n$ and $a_n\to0$, then $ c_n \to0$

Published on 16 Apr 2026 - 23:56

score 1.3k · Answer 6 · 2026-04-14 01:14:35

1.3k

Views

The characterization of an interval theorem.

Published on 14 Apr 2026 - 1:14

score 64 · Answer 7 · 2026-04-07 14:49:09

64

Views

Let $f:\mathbb{R}^2\to \mathbb{R}$ be of class $C^1$, with $f(2,-1)=-1$. Set $G(x,y,u)=f(x,y)+u^2, H(x,y,u)= ux+3y^3+u^3$.

Published on 07 Apr 2026 - 14:49

score 169 · Answer 8 · 2026-04-29 12:54:17

169

Views

Prove an integration inequality $\int_{0}^{1}\,\left(\int_{0}^{x}\,f(y)\,{\rm d}y\right)^2{\rm d}x\leqslant -\frac{mM}{6(M-m)^2}(3m^2-8mM+3M^2)$

Published on 29 Apr 2026 - 12:54

score 114 · Answer 9 · 2026-04-15 18:12:51

114

Views

Functions $f: \mathbb{R}^n \to \mathbb{R}$ such that $|f(x) -f(y)| \le C \prod_{i=1}^n |x_i - y_i|^{\alpha_i}$

Published on 15 Apr 2026 - 18:12

score 41 · Answer 10 · 2026-04-12 12:10:09

41

Views

Counter argument for the characterization of intervals.

Published on 12 Apr 2026 - 12:10

score 468 · Answer 11 · 2026-04-12 05:35:02

468

Views

What is the value of $\lim_{(x,y,z)\rightarrow(0,0,0)}\log(\frac{x}{yz})$?

Published on 12 Apr 2026 - 5:35

score 122 · Answer 12 · 2026-04-14 20:28:39

122

Views

Prove that this set is closed

Published on 14 Apr 2026 - 20:28

score 81 · Answer 13 · 2026-04-29 12:16:44

81

Views

Convergence of sequence of functions to x^2

Published on 29 Apr 2026 - 12:16

score 55 · Answer 14 · 2026-04-09 09:33:51

55

Views

Two definitions of convergence?

Published on 09 Apr 2026 - 9:33

score 270 · Answer 15 · 2026-04-16 05:03:22

270

Views

Dimension of B(T), the set of all bounded functions in a non-empty set T.

Published on 16 Apr 2026 - 5:03

List Question

Every two norms on a finite dimensional (real or complex) vector space $V$ are equivalent.

Consider the bisection method starting with the interval $[1.5, 3.5]$

Show that $(a,b)\times (c,d)$ is an open set in $\mathbb{R}^2$ with the Euclidian metric.

Let $T: V \to W$ be a linear map. Let $V$ be finite dimensional. Then $T$ is continuous.

If $\sin c_n= 3c_n-a_n$ and $a_n\to0$, then $ c_n \to0$

The characterization of an interval theorem.

Let $f:\mathbb{R}^2\to \mathbb{R}$ be of class $C^1$, with $f(2,-1)=-1$. Set $G(x,y,u)=f(x,y)+u^2, H(x,y,u)= ux+3y^3+u^3$.

Prove an integration inequality $\int_{0}^{1}\,\left(\int_{0}^{x}\,f(y)\,{\rm d}y\right)^2{\rm d}x\leqslant -\frac{mM}{6(M-m)^2}(3m^2-8mM+3M^2)$

Functions $f: \mathbb{R}^n \to \mathbb{R}$ such that $|f(x) -f(y)| \le C \prod_{i=1}^n |x_i - y_i|^{\alpha_i}$

Counter argument for the characterization of intervals.

What is the value of $\lim_{(x,y,z)\rightarrow(0,0,0)}\log(\frac{x}{yz})$?

Prove that this set is closed

Convergence of sequence of functions to x^2

Two definitions of convergence?

Dimension of B(T), the set of all bounded functions in a non-empty set T.

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