Question

Is it possible to define the eigenvalues of a linear operator without first defining the matrix of the linear operator?

score 100 · Answer 1 · 2026-04-08 23:31:30

100

Views

Is it possible to define the eigenvalues of a linear operator without first defining the matrix of the linear operator?

Published on 08 Apr 2026 - 23:31

score 420 · Answer 2 · 2026-04-15 03:21:26

420

Views

Prove that for all $x$, $\sum_{j=0}^{n}ℓ_j(x)=1$

Published on 15 Apr 2026 - 3:21

score 67 · Answer 3 · 2026-04-16 12:29:44

67

Views

Given eigenvectors and eigenvalues of a matrix $A$, how to find its inverse and the limit of $A^nv$?

Published on 16 Apr 2026 - 12:29

score 83 · Answer 4 · 2026-04-23 05:12:15

83

Views

Does this property imply total unimodularity?

Published on 23 Apr 2026 - 5:12

score 554 · Answer 5 · 2026-04-12 16:01:44

554

Views

An open subset of $\mathbb{R}^n$ is not diffeomorphic to an open subset of $\mathbb{R}^m$

Published on 12 Apr 2026 - 16:01

score 83 · Answer 6 · 2026-04-19 15:24:24

83

Views

What is the rank of $B$?

Published on 19 Apr 2026 - 15:24

score 1.3k · Answer 7 · 2026-04-20 00:47:56

1.3k

Views

What is the relation between general solution of a differential equation and null space?

Published on 20 Apr 2026 - 0:47

score 115 · Answer 8 · 2026-04-11 21:22:44

115

Views

Does polar decomposition give commutative answer, i.e. it is group isomorphism?

Published on 11 Apr 2026 - 21:22

score 167 · Answer 9 · 2026-04-09 02:09:35

167

Views

Eigenvalue for a linear operator involving derivates

Published on 09 Apr 2026 - 2:09

score 329 · Answer 10 · 2026-04-16 11:05:06

329

Views

Prove that $T$ is invertible if $(T\circ T)+T −2I_V = 0$

Published on 16 Apr 2026 - 11:05

score 717 · Answer 11 · 2026-04-22 12:03:24

717

Views

Calculate Smith normal form, cyclic group decomposition

Published on 22 Apr 2026 - 12:03

score 583 · Answer 12 · 2026-04-13 07:49:53

583

Views

How to prove that if $f^3 = f$, $f$ is diagonalizable?

Published on 13 Apr 2026 - 7:49

score 133 · Answer 13 · 2026-04-12 23:12:30

133

Views

Monotone Property of Matrix

Published on 12 Apr 2026 - 23:12

score 441 · Answer 14 · 2026-04-15 15:09:36

441

Views

$\text{rk}(AB)=\text{rk}(BA)$ generally

Published on 15 Apr 2026 - 15:09

score 92 · Answer 15 · 2026-04-12 03:32:19

92

Views

How do I show that this square matrix has this relationship?

Published on 12 Apr 2026 - 3:32

List Question

Is it possible to define the eigenvalues of a linear operator without first defining the matrix of the linear operator?

Prove that for all $x$, $\sum_{j=0}^{n}ℓ_j(x)=1$

Given eigenvectors and eigenvalues of a matrix $A$, how to find its inverse and the limit of $A^nv$?

Does this property imply total unimodularity?

An open subset of $\mathbb{R}^n$ is not diffeomorphic to an open subset of $\mathbb{R}^m$

What is the rank of $B$?

What is the relation between general solution of a differential equation and null space?

Does polar decomposition give commutative answer, i.e. it is group isomorphism?

Eigenvalue for a linear operator involving derivates

Prove that $T$ is invertible if $(T\circ T)+T −2I_V = 0$

Calculate Smith normal form, cyclic group decomposition

How to prove that if $f^3 = f$, $f$ is diagonalizable?

Monotone Property of Matrix

$\text{rk}(AB)=\text{rk}(BA)$ generally

How do I show that this square matrix has this relationship?

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