User JustANoob

7 votes

2 answers

95 views

Prove that $\exists c > 0$ such that $||f||_2 \le c ||T(f)||_{\infty}$

asked Dec 21, 2021 at 10:04

5 votes

2 answers

4k views

Why do $A$ and $A^TA$ have the same row space?

linear-algebra matrices

asked Sep 8, 2017 at 8:46

4 votes

5 answers

237 views

Which points on the curve $5x^2+4xy+2y^2-6=0$ are closest to the origin.

calculus multivariable-calculus optimization quadratics lagrange-multiplier

asked Jan 12, 2018 at 12:39

4 votes

1 answer

105 views

Understanding weakly dense.

functional-analysis weak-convergence

asked Jan 9 at 11:27

3 votes

1 answer

26 views

Redundancy in the definition of the resolvet set?

functional-analysis normed-spaces spectral-theory

asked Jan 10 at 20:29

3 votes

1 answer

173 views

$\sigma(T)$ is finite $\iff \exists p\in P: p(T) = 0$

functional-analysis eigenvalues-eigenvectors hilbert-spaces

asked Dec 30, 2021 at 21:46

3 votes

0 answers

54 views

Show that $T$ is isometric and not surjective. Proof validation.

functional-analysis solution-verification normed-spaces isometry

asked Dec 19, 2021 at 14:16

3 votes

1 answer

49 views

$T$ is continuous $\iff \forall (x_1, x_2,..), x_i \in X, x_i \to^w x \implies T(x_i) \to^w T(x)$

functional-analysis solution-verification banach-spaces weak-convergence dual-spaces

asked Dec 20, 2021 at 10:16

3 votes

2 answers

114 views

Spectrum of $Tf(x) := \frac{1}{x}\int_{0}^{x}f(t)dt $

functional-analysis spectral-theory

asked Nov 9, 2021 at 16:17

3 votes

1 answer

114 views

Distribution of $Z_n=n \log\left(\frac{\max\left(X_{(n)},Y_{(n)}\right)}{\min\left(X_{(n)},Y_{(n)}\right)}\right)$

probability probability-theory probability-distributions order-statistics

asked Feb 13, 2018 at 12:00

3 votes

1 answer

676 views

Prove strict convex norm equivalence

convex-analysis normed-spaces

asked Mar 2, 2018 at 14:19

3 votes

1 answer

32 views

Exists an $h$ such that $\lVert u + hv \rVert_{\infty}= \max_{x \in U}|u(x)+hv(x)|$

normed-spaces supremum-and-infimum

asked Mar 19, 2018 at 18:02

3 votes

0 answers

80 views

Show that $Y_1$ and $Y_2$ are independent $N(0, 1)$-distributed random variables. [duplicate]

probability random-variables normal-distribution

asked Aug 17, 2018 at 12:52

3 votes

2 answers

588 views

Distribution of $X\sqrt {2Y}$ where $X\sim N (0,1)$ and $Y\sim \operatorname{Exp} (1)$

probability probability-distributions change-of-variable

asked Jul 29, 2017 at 22:41

2 votes

1 answer

66 views

Find the distribution of $Y$ given $p_{X}$ and $ p_{Y \mid X}$

probability probability-theory probability-distributions summation

asked Aug 1, 2017 at 16:15

2 votes

1 answer

446 views

Prove that the dimension of the eigenspace corresponding to the eigenvalue $\lambda=1$ of $H$ is at least the number of the clusters..

linear-algebra eigenvalues-eigenvectors matrix-rank page-rank

asked Sep 28, 2017 at 16:28

2 votes

1 answer

161 views

Calculate flux integral

integration stokes-theorem greens-theorem change-of-variable

asked Dec 26, 2017 at 13:50

2 votes

1 answer

531 views

Expected value of the total waiting time of all passengers catching a train.

probability-theory random-variables poisson-process

asked Aug 28, 2018 at 8:59

2 votes

2 answers

110 views

Find different $f_1,f_2 \in F$ such that $\lVert f_1 \rVert = \lVert f_2 \rVert=1$ and $\lVert f_1 + f_2 \rVert =2$

linear-algebra convex-analysis normed-spaces

asked Feb 23, 2018 at 15:33

2 votes

1 answer

96 views

Connected Dirichlet and Neumann conditions

numerical-methods partial-derivative laplacian

asked Oct 9, 2018 at 6:40

2 votes

1 answer

58 views

Show that $\exists L \in (l^\infty)'$ such that $\forall f \in C([0,1]): \int\limits_{0}^{1}f(t)dt = L(T(f))$.

functional-analysis dual-spaces

asked Dec 19, 2021 at 20:28

2 votes

0 answers

33 views

A matrix $A$ is $K$-irreducible if and only if no eigenvector lies on $\partial K$.

linear-algebra proof-explanation invariant-subspace convex-cone nonnegative-matrices

asked Jan 4 at 8:29

2 votes

1 answer

52 views

Dense and weakly dense, sequentially speaking.

general-topology functional-analysis weak-convergence

asked Jan 10 at 15:53

2 votes

0 answers

26 views

Map bounded if composition is bounded. (Proof verification)

functional-analysis solution-verification normed-spaces

asked Jan 6 at 20:47

2 votes

2 answers

97 views

Probability of $x$ being rational

real-analysis probability sequences-and-series

asked Apr 21 at 8:09

1 vote

1 answer

44 views

Equicontinuity, compactness and uniform convergence.

real-analysis general-topology compactness uniform-convergence

asked Apr 25 at 13:07

1 vote

0 answers

33 views

Show that $\dim(Z) < \infty$ if $Z \subset T(X)$ for compact $T$

functional-analysis banach-spaces compact-operators open-map

asked Jan 11 at 15:45

1 vote

1 answer

61 views

Show that $T f(x) = \frac{1}{x^2}\int\limits_0^x t f(t) dt$ is not compact.

solution-verification banach-spaces spectral-theory

asked Dec 28, 2021 at 11:01

1 vote

1 answer

25 views

$\nexists y \in l^1$ such that $\forall x \in S: L(x) = \sum\limits_{n\ge 1}(x y)\lbrack n \rbrack$

normed-spaces dual-spaces

asked Dec 19, 2021 at 8:47

1 vote

0 answers

25 views

References on nonnegative matrices

matrices reference-request book-recommendation nonnegative-matrices

asked Dec 12, 2021 at 17:05

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80 Questions

Prove that $\exists c > 0$ such that $||f||_2 \le c ||T(f)||_{\infty}$

Why do $A$ and $A^TA$ have the same row space?

Which points on the curve $5x^2+4xy+2y^2-6=0$ are closest to the origin.

Understanding weakly dense.

Redundancy in the definition of the resolvet set?

$\sigma(T)$ is finite $\iff \exists p\in P: p(T) = 0$

Show that $T$ is isometric and not surjective. Proof validation.

$T$ is continuous $\iff \forall (x_1, x_2,..), x_i \in X, x_i \to^w x \implies T(x_i) \to^w T(x)$

Spectrum of $Tf(x) := \frac{1}{x}\int_{0}^{x}f(t)dt $

Distribution of $Z_n=n \log\left(\frac{\max\left(X_{(n)},Y_{(n)}\right)}{\min\left(X_{(n)},Y_{(n)}\right)}\right)$

Prove strict convex norm equivalence

Exists an $h$ such that $\lVert u + hv \rVert_{\infty}= \max_{x \in U}|u(x)+hv(x)|$

Show that $Y_1$ and $Y_2$ are independent $N(0, 1)$-distributed random variables. [duplicate]

Distribution of $X\sqrt {2Y}$ where $X\sim N (0,1)$ and $Y\sim \operatorname{Exp} (1)$

Find the distribution of $Y$ given $p_{X}$ and $ p_{Y \mid X}$

Prove that the dimension of the eigenspace corresponding to the eigenvalue $\lambda=1$ of $H$ is at least the number of the clusters..

Calculate flux integral

Expected value of the total waiting time of all passengers catching a train.

Find different $f_1,f_2 \in F$ such that $\lVert f_1 \rVert = \lVert f_2 \rVert=1$ and $\lVert f_1 + f_2 \rVert =2$

Connected Dirichlet and Neumann conditions

Show that $\exists L \in (l^\infty)'$ such that $\forall f \in C([0,1]): \int\limits_{0}^{1}f(t)dt = L(T(f))$.

A matrix $A$ is $K$-irreducible if and only if no eigenvector lies on $\partial K$.

Dense and weakly dense, sequentially speaking.

Map bounded if composition is bounded. (Proof verification)

Probability of $x$ being rational

Equicontinuity, compactness and uniform convergence.

Show that $\dim(Z) < \infty$ if $Z \subset T(X)$ for compact $T$

Show that $T f(x) = \frac{1}{x^2}\int\limits_0^x t f(t) dt$ is not compact.

$\nexists y \in l^1$ such that $\forall x \in S: L(x) = \sum\limits_{n\ge 1}(x y)\lbrack n \rbrack$

References on nonnegative matrices