# Tagged Questions

For questions about matrix diagonalization, that is, writing a matrix, a bilinear form or an operator into a "basis" making this one diagonal. This tag is **NOT** for diagonalization arguments from logic and set theory.

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### Prove that matrix $A$ diagonalizable if $A^2=I$ using characteristic polynomial

Prove that the matrix $A$ is diagonalizable if $A^2=I$ using characteristic polynomial I saw an answer that used the minimal polynomial of $A$. Can that be proven without using minimal polynomial? ...
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### Given a symmetric matrix $A$, find $P$ such that $P^T A P$ is a diagonal matrix

Given $$A =\begin{pmatrix} 0 & 3 & 0 \\ 3 & 0 & 4 \\ 0 & 4 & 0\end{pmatrix}$$ find a matrix $P$ such that $P^T A P$ orthogonally diagonalizes $A$. Verify that $P^TAP$ is ...
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### Power method and convergence

I am working on some practice problems for the convergence of power method for some given recursion relationship and I am trying to generalize/reflect on the question after having been stuck on the ...
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### Recursion relationship and linear algebra

I wanted to confirm my intuition about a problem that I got wrong relating to an application of the power method to recursion relations. The question is as follows: For the context of the question, ...
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### Minimal polynomial and diagonalizable matrix: property

Quick question We know that if a matrix/linear transformation in a space has dimension n and its minimal polynomial has k different roots with algebraic multiplicity 1, that the matrix/linear ...
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### low rank approximations and diagonalization

I would like to discuss or hear an opinion about the following. Given is the (hermitian) $n\times n$ matrix $A = D+M V M^{\dagger}$ with D diagonal. I would like to calculate the eigenvalues (and ...
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### Finding an invertible matrix.

I want to find an invertible matrix $P$ where $P^tAP$ is a diagonal matrix. $$A=\begin{pmatrix} 1 & 2 & 1 \\ 2 & 0 & 2 \\ 1 & 2 & 1 \end{pmatrix}$$ I have calculated ...