Question

If $x^TAx$ = $x^TBx$ for all $x\in \mathbb R^n$. Then what can I say about the matrices? Are they congruent to each other?

score 5.7k · Answer 1 · 2026-04-13 16:48:37

5.7k

Views

If $x^TAx$ = $x^TBx$ for all $x\in \mathbb R^n$. Then what can I say about the matrices? Are they congruent to each other?

Published on 13 Apr 2026 - 16:48

score 64 · Answer 2 · 2026-04-13 02:08:57

64

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What is exact definition of 'wronskian' for ODE

Published on 13 Apr 2026 - 2:08

score 60 · Answer 3 · 2026-04-13 02:35:31

60

Views

Is this tiny conjecture true concerning $\alpha$ true?

Published on 13 Apr 2026 - 2:35

score 37 · Answer 4 · 2026-04-13 10:51:29

37

Views

Given a mapping for $\mathbb R^2 \to \mathbb R^3 , A,$ find new basis for $\mathbb R^2$ and $\mathbb R^3$ such that the mapping is now diagonal

Published on 13 Apr 2026 - 10:51

score 1.6k · Answer 5 · 2026-04-08 17:35:48

1.6k

Views

Matrix with only real eigenvalues is similar to upper triangular matrix

Published on 08 Apr 2026 - 17:35

score 3.5k · Answer 6 · 2026-04-12 07:59:44

3.5k

Views

What's a selection matrix?

Published on 12 Apr 2026 - 7:59

score 1.9k · Answer 7 · 2026-03-25 04:43:55

1.9k

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Area of parallelograms in $\mathbb{R}^n$ (or more generally, the volume of parallelotopes in $\mathbb{R}^n$ )

Published on 25 Mar 2026 - 4:43

score 134 · Answer 8 · 2018-04-12 17:24:30

134

Views

Derivative w.r.t. matrix

Published on 12 Apr 2018 - 17:24

score 1k · Answer 9 · 2026-03-25 09:32:09

1k

Views

Classify up to similarity all $n\times n$ complex matrices such that $A^n=I$

Published on 25 Mar 2026 - 9:32

score 85 · Answer 10 · 2026-04-13 11:53:26

85

Views

Is spectral decomposition a differentiable function?

Published on 13 Apr 2026 - 11:53

score 322 · Answer 11 · 2026-04-13 07:48:28

322

Views

On problem regarding the quadratic form $yx+z^2$.

Published on 13 Apr 2026 - 7:48

score 177 · Answer 12 · 2026-04-08 17:38:15

Find the precise conditions on $a,b,c$ so that $\left[\begin{smallmatrix}a&b\\c&d\end{smallmatrix}\right]$ is nonnegative definite.

score 123 · Answer 13 · 2026-03-27 16:22:51

123

Views

Prove that $\{I, T, ..., T^k\}$ is linearly dependent (LD) if and only if $\forall v \colon \{v, T(v), ..., T^k(v)\}$ is LD.

Published on 27 Mar 2026 - 16:22

score 5.4k · Answer 14 · 2026-04-13 01:14:00

5.4k

Views

Is it possible for an eigenspace to have dimension $0$?

Published on 13 Apr 2026 - 1:14

score 1.6k · Answer 15 · 2026-03-28 13:42:22

1.6k

Views

Does the algebraic multiplicity of all the eigenvalues of a matrix always add up to the dimension of the matrix?

Published on 28 Mar 2026 - 13:42

List Question

If $x^TAx$ = $x^TBx$ for all $x\in \mathbb R^n$. Then what can I say about the matrices? Are they congruent to each other?

What is exact definition of 'wronskian' for ODE

Is this tiny conjecture true concerning $\alpha$ true?

Given a mapping for $\mathbb R^2 \to \mathbb R^3 , A,$ find new basis for $\mathbb R^2$ and $\mathbb R^3$ such that the mapping is now diagonal

Matrix with only real eigenvalues is similar to upper triangular matrix

What's a selection matrix?

Area of parallelograms in $\mathbb{R}^n$ (or more generally, the volume of parallelotopes in $\mathbb{R}^n$ )

Derivative w.r.t. matrix

Classify up to similarity all $n\times n$ complex matrices such that $A^n=I$

Is spectral decomposition a differentiable function?

On problem regarding the quadratic form $yx+z^2$.

Find the precise conditions on $a,b,c$ so that $\left[\begin{smallmatrix}a&b\\c&d\end{smallmatrix}\right]$ is nonnegative definite.

Prove that $\{I, T, ..., T^k\}$ is linearly dependent (LD) if and only if $\forall v \colon \{v, T(v), ..., T^k(v)\}$ is LD.

Is it possible for an eigenspace to have dimension $0$?

Does the algebraic multiplicity of all the eigenvalues of a matrix always add up to the dimension of the matrix?

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