List questions from self-learning

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Why does $\operatorname{rank}(\mathbf{X})$ equal $\operatorname{rank}(\mathbf{X^TX})$? What is $\dim(\mathbf{X^TX})$?

Published on 01 Jan 2014 - 10:14

87

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Boundary Value Problem (Separation of Variables)

Published on 09 Apr 2026 - 14:06

357

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Exercise Real Analysis

Published on 10 Apr 2026 - 19:05

2.1k

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Introductory Algebra Book Suggestions

Published on 12 Apr 2026 - 13:20

220

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Will a bounded sequence in $\mathbb{R}$ necessarily induce a compact subset of $\mathbb{R}$?

Published on 12 Apr 2026 - 14:33

4.6k

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How to linearize a nonlinear ODE around its equilibrium?

Published on 12 Apr 2026 - 1:33

97

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Zeta function in complex analysis.

Published on 09 Apr 2026 - 10:16

283

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Why can't the interval construction argument used to show $\mathbb{R}$ is uncountable be used for other infinite sets?

Published on 04 Jan 2014 - 16:37

204

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Find $\displaystyle \sum_{k=1}^{\infty}\frac{1}{z_k^2}$

Published on 05 Jan 2014 - 0:08

3.2k

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Introduction to ring theory?

Published on 08 Apr 2026 - 21:45

12.4k

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What does countable union mean?

Published on 09 Apr 2026 - 12:41

38

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Find an integral expression for $\Gamma'(z)$ for $\Re z\gt 0$

Published on 12 Apr 2026 - 19:22

200

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Derive a perturbation of period $2\pi$, to order $\epsilon$

Published on 28 Mar 2026 - 7:53

1.5k

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Gamma function can be extended as a meromorphic function

Published on 12 Apr 2026 - 18:01

66

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show $\int g\log (g/f)$ is $0$ only if $g=f$ almost everywhere

Published on 06 Jan 2014 - 11:34

List Question

Why does $\operatorname{rank}(\mathbf{X})$ equal $\operatorname{rank}(\mathbf{X^TX})$? What is $\dim(\mathbf{X^TX})$?

Boundary Value Problem (Separation of Variables)

Exercise Real Analysis

Introductory Algebra Book Suggestions

Will a bounded sequence in $\mathbb{R}$ necessarily induce a compact subset of $\mathbb{R}$?

How to linearize a nonlinear ODE around its equilibrium?

Zeta function in complex analysis.

Why can't the interval construction argument used to show $\mathbb{R}$ is uncountable be used for other infinite sets?

Find $\displaystyle \sum_{k=1}^{\infty}\frac{1}{z_k^2}$

Introduction to ring theory?

What does countable union mean?

Find an integral expression for $\Gamma'(z)$ for $\Re z\gt 0$

Derive a perturbation of period $2\pi$, to order $\epsilon$

Gamma function can be extended as a meromorphic function

show $\int g\log (g/f)$ is $0$ only if $g=f$ almost everywhere

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