List questions from diagonalization

Published on 31 Mar 2026 - 12:54

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For classification of quadratic forms with orthogonal diagonalization, why do we need a rotation?

Published on 03 Feb 2023 - 9:32

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When $v, Av, A^2v$ are linearly independent

Published on 05 Feb 2023 - 18:58

819

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Diagonalization of the matrix $\begin{pmatrix}1&-3&3\\3&-5&3\\6&-6&4\end{pmatrix}$

Published on 10 Feb 2023 - 9:16

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Find the $n$th power of a 3-by-3 circulant matrix

Published on 25 Mar 2026 - 6:04

106

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Exercise 7, Section 7.1 of Hoffman’s Linear Algebra

Published on 15 Feb 2023 - 21:59

606

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When is the product of two matrices diagonalizable?

Published on 17 Feb 2023 - 3:04

193

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Diagonalising a $2 \times 2$ symmetric matrix

Published on 30 Mar 2026 - 3:36

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Real normal matrix which is diagonalizable over $\mathbb{R}$ but not unitary diagonalizable over $\mathbb{R}$.

Published on 22 Feb 2023 - 10:27

78

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How to diagonalize this (close-to-diagonal) matrix fast?

Published on 31 Mar 2026 - 14:24

98

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Functional square root of a function $F([a,b])=[1−br+a,1−br+a+b]$.

Published on 27 Feb 2023 - 9:18

533

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Can we use the singular value decomposition to compute the matrix exponential for a non-diagonalisable matrix?

Published on 27 Mar 2026 - 14:28

39

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Is a real-symmetric matrix diagonalizable by a special-orthogonal matrix?

Published on 06 Mar 2023 - 22:34

164

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Proof for $X^3=I$ $\implies$ $X$ is diagonalizable.

Published on 07 Mar 2023 - 14:50

255

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Finding the eigenvalues of a 9x9 matrix

Published on 09 Mar 2023 - 16:40

List Question

Solving a $3\times3$ non-linear system

For classification of quadratic forms with orthogonal diagonalization, why do we need a rotation?

When $v, Av, A^2v$ are linearly independent

Diagonalization of the matrix $\begin{pmatrix}1&-3&3\\3&-5&3\\6&-6&4\end{pmatrix}$

Find the $n$th power of a 3-by-3 circulant matrix

Exercise 7, Section 7.1 of Hoffman’s Linear Algebra

When is the product of two matrices diagonalizable?

Diagonalising a $2 \times 2$ symmetric matrix

Real normal matrix which is diagonalizable over $\mathbb{R}$ but not unitary diagonalizable over $\mathbb{R}$.

How to diagonalize this (close-to-diagonal) matrix fast?

Functional square root of a function $F([a,b])=[1−br+a,1−br+a+b]$.

Can we use the singular value decomposition to compute the matrix exponential for a non-diagonalisable matrix?

Is a real-symmetric matrix diagonalizable by a special-orthogonal matrix?

Proof for $X^3=I$ $\implies$ $X$ is diagonalizable.

Finding the eigenvalues of a 9x9 matrix

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