Eigenvalue calculator

Find eigenvalues and eigenvectors of a matrix. Includes characteristic polynomial, diagonalization, and step-by-step solutions.

Matrix

Eigenvalues and eigenvectors

Av = λv — an eigenvector v is scaled by factor λ (eigenvalue) when multiplied by A.

Finding eigenvalues

Solve det(A − λI) = 0. For 2×2: λ² − tr(A)λ + det(A) = 0.

Applications

Google PageRank, quantum mechanics, vibration analysis, PCA in machine learning, stability analysis of systems.

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