List questions from linear-algebra

Published on 08 Feb 2018 - 8:01

92

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Can a positive definite matrix $S$ always be expressed in the form $S=A^TA$?

Published on 08 Feb 2018 - 8:40

321

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An efficient way to calculate probabilities for Markov chain/Random walks on a graph

Published on 25 Mar 2026 - 1:16

2.4k

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Does an n by n Hermitian matrix always has n independent eigenvectors?

Published on 26 Mar 2026 - 14:29

66

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Diagnolization of a matrix in R3

Published on 24 Mar 2026 - 20:41

2.2k

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Linear Algebra: Residual $A x - b$

Published on 29 Mar 2026 - 19:51

91

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Determine whether transformation is linear and finding its matrix?

Published on 27 Mar 2026 - 5:36

120

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Understanding Karlin's Proof of Perron's Theorem.

Published on 08 Feb 2018 - 13:47

69

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Find all the triples $(x,y,z)$ $\in$ $\Bbb R^+_0$ that verifies the following equation system

Published on 29 Mar 2026 - 16:03

30

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Transformation not defined for two different dimensions

Published on 08 Feb 2018 - 15:12

162

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Proof Explanation: $\rho(\tau)=\rho(\tau\sigma)+dim[Im(\sigma)\cap K(\tau)]$

Published on 25 Mar 2026 - 15:12

318

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What is the rank of a linear transformation $f: \mathbb{R}^3 \rightarrow \mathbb{R}^3$ such that $ \operatorname{Ker} f \leqslant \operatorname{Im}f$?

Published on 27 Mar 2026 - 5:41

281

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Matrix Determinant after row changes

Published on 25 Mar 2026 - 22:01

120

Views

Linearly independent coordinates

Published on 24 Mar 2026 - 22:06

66

Views

Making matrices look the same w.r.t different basis's

Published on 08 Feb 2018 - 18:51

List Question

Invertibility and rank

Can a positive definite matrix $S$ always be expressed in the form $S=A^TA$?

An efficient way to calculate probabilities for Markov chain/Random walks on a graph

Does an n by n Hermitian matrix always has n independent eigenvectors?

Diagnolization of a matrix in R3

Linear Algebra: Residual $A x - b$

Determine whether transformation is linear and finding its matrix?

Understanding Karlin's Proof of Perron's Theorem.

Find all the triples $(x,y,z)$ $\in$ $\Bbb R^+_0$ that verifies the following equation system

Transformation not defined for two different dimensions

Proof Explanation: $\rho(\tau)=\rho(\tau\sigma)+dim[Im(\sigma)\cap K(\tau)]$

What is the rank of a linear transformation $f: \mathbb{R}^3 \rightarrow \mathbb{R}^3$ such that $ \operatorname{Ker} f \leqslant \operatorname{Im}f$?

Matrix Determinant after row changes

Linearly independent coordinates

Making matrices look the same w.r.t different basis's

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