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Eigenvalues and Eigenvectors

★★★★☆Undergraduate

📖Definition

For matrix A, λ is an eigenvalue and v is an eigenvector if Av = λv.

Av = λ v

Eigenvalue equation

det(A - λ I) = 0

Characteristic equation

예제 1★★★★☆

Find the eigenvalues of A = [[2, 1], [1, 2]].

Developed from work by Euler and Lagrange, formalized by Hilbert.

Quantum mechanics, vibration modes

PCA (Principal Component Analysis)

Google search algorithm

#linear-algebra#eigenvalue#eigenvector#advanced