Math Problem Statement

Solution

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Math Problem Analysis

Mathematical Concepts

Linear Algebra
Matrix Diagonalization
Eigenvalues and Eigenvectors
Rational Form
Jordan Canonical Form

Formulas

Characteristic Polynomial: det(A - λI) = 0
Eigenvector Equation: (A - λI)v = 0
Matrix Diagonalization: P^{-1}AP = D

Theorems

Cayley-Hamilton Theorem
Spectral Theorem (for diagonalization)
Jordan Canonical Form Theorem

Suitable Grade Level

Undergraduate Linear Algebra