Question

Direction vectors are linearly dependent, if $D_vf(x)=D_wf(x)=0$ with $\operatorname{grad} f(x)\neq 0$

score 42 · Answer 1 · 2018-08-25 01:03:45

42

Views

Direction vectors are linearly dependent, if $D_vf(x)=D_wf(x)=0$ with $\operatorname{grad} f(x)\neq 0$

Published on 25 Aug 2018 - 1:03

score 1.8k · Answer 2 · 2018-08-25 01:57:53

1.8k

Views

Let $x,y$ be numbers and $xy = 1$, show that $x$ and $y$ are never zero

Published on 25 Aug 2018 - 1:57

score 47 · Answer 3 · 2018-08-25 02:18:38

47

Views

Check this measure theory argument

Published on 25 Aug 2018 - 2:18

score 50 · Answer 4 · 2018-08-25 05:08:42

50

Views

Injectivity means $a_1 = a_2 \Longleftrightarrow f(a_1) = f(a_2)$? Structuring Proof of Injectivity.

Published on 25 Aug 2018 - 5:08

score 56 · Answer 5 · 2018-08-25 08:37:15

56

Views

Check measure theory argument

Published on 25 Aug 2018 - 8:37

score 58 · Answer 6 · 2018-08-25 09:30:10

58

Views

Proof verification: Let $f:O\subset \Bbb{R}^n\to\Bbb{R}$ be a $C^3$ function. If $A$ is positive, then $x_0$ is a local minimum.

Published on 25 Aug 2018 - 9:30

score 143 · Answer 7 · 2026-03-27 01:42:14

143

Views

Learning Real Analysis outside a classroom setting

Published on 27 Mar 2026 - 1:42

score 98 · Answer 8 · 2018-08-25 16:15:34

98

Views

Maximum of the function $f(x, y)=(x^2+y^2)e^{-x^2-y^2}$.

Published on 25 Aug 2018 - 16:15

score 53 · Answer 9 · 2018-08-25 18:56:34

53

Views

$f'(0)<0, f''(x)<0$ then for $\alpha\in(0,1)$, $f(x)\le f(0) + \alpha x f'(0)$ for all $x>0$

Published on 25 Aug 2018 - 18:56

score 170 · Answer 10 · 2026-03-27 06:12:32

170

Views

$f(\overline{x})=0$ but $\nabla^2 f(\overline{x})$ is not semidefinite positive. Prove there exists a descent direction

Published on 27 Mar 2026 - 6:12

score 32 · Answer 11 · 2026-03-25 17:21:42

32

Views

substitution in $\mathbb R^n$ :$\int_{\varphi(U)} f=\int_U f(\psi)|\det J_\psi|$. Why if taking $U$ closed instead of open the formula still hold?

Published on 25 Mar 2026 - 17:21

score 878 · Answer 12 · 2026-03-25 20:42:03

878

Views

Prove that the only eigenvalue of a unipotent matrix is 1.

Published on 25 Mar 2026 - 20:42

score 2.7k · Answer 13 · 2026-04-01 08:03:53

2.7k

Views

Is modus ponens a tautology?

Published on 01 Apr 2026 - 8:03

score 96 · Answer 14 · 2018-08-26 07:55:04

96

Views

Checking work on three successive questions in Cohn, Measure Theory

Published on 26 Aug 2018 - 7:55

score 106 · Answer 15 · 2026-02-22 21:41:04

106

Views

Constructing a Bounded Solution using Frobenius' Method

Published on 22 Feb 2026 - 21:41

List Question

Direction vectors are linearly dependent, if $D_vf(x)=D_wf(x)=0$ with $\operatorname{grad} f(x)\neq 0$

Let $x,y$ be numbers and $xy = 1$, show that $x$ and $y$ are never zero

Check this measure theory argument

Injectivity means $a_1 = a_2 \Longleftrightarrow f(a_1) = f(a_2)$? Structuring Proof of Injectivity.

Check measure theory argument

Proof verification: Let $f:O\subset \Bbb{R}^n\to\Bbb{R}$ be a $C^3$ function. If $A$ is positive, then $x_0$ is a local minimum.

Learning Real Analysis outside a classroom setting

Maximum of the function $f(x, y)=(x^2+y^2)e^{-x^2-y^2}$.

$f'(0)<0, f''(x)<0$ then for $\alpha\in(0,1)$, $f(x)\le f(0) + \alpha x f'(0)$ for all $x>0$

$f(\overline{x})=0$ but $\nabla^2 f(\overline{x})$ is not semidefinite positive. Prove there exists a descent direction

substitution in $\mathbb R^n$ :$\int_{\varphi(U)} f=\int_U f(\psi)|\det J_\psi|$. Why if taking $U$ closed instead of open the formula still hold?

Prove that the only eigenvalue of a unipotent matrix is 1.

Is modus ponens a tautology?

Checking work on three successive questions in Cohn, Measure Theory

Constructing a Bounded Solution using Frobenius' Method

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