# Diagonalize a symmetric matrix

> ML Prep screening item.

- Stable ID: `math-la-06-spectral-power`
- Collection: screening
- Area: Mathematics
- Topic: Linear Algebra
- Origin: original
- Difficulty: medium
- Expected time: 5 minutes
- Skills: eigenvalues, eigenvectors, diagonalization, symmetric-matrices
- Item JSON: https://mlprep.iwase.dev/item/math-la-06-spectral-power.json

## Problem

For $A=\begin{bmatrix}2&1\\1&2\end{bmatrix}$, find an orthogonal diagonalization
and use it to compute $A^3$ without repeated matrix multiplication.


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