Math Problem Statement
For n ≥ 2, the eigenvalues of Cn are 2 cos 2π k n , k = 1,..., n
Solution
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Math Problem Analysis
Mathematical Concepts
Linear Algebra
Eigenvalues
Circulant Matrices
Discrete Fourier Transform (DFT)
Formulas
Eigenvalues of Cyclic Matrix: \( \lambda_k = 2 \cos \left(\frac{2\pi k}{n}\right) \)
Theorems
Properties of Circulant Matrices
Fourier Series and Eigenvalues
Suitable Grade Level
Advanced Undergraduate
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