Eigenvalue Problems

December 30, 2025 · View on GitHub

Learn how to solve eigenvalue problems using LAPACK.

What You'll Learn

  • Understanding eigenvalues and eigenvectors
  • Computing eigenvalues
  • Computing eigenvectors
  • Applications of eigenvalue problems

Prerequisites

Theory

For matrix A, find λ and v such that:

Av = λv

Where:

  • λ is an eigenvalue (scalar)
  • v is an eigenvector (vector)

Computing Eigenvalues

Symmetric Matrices (dsyev)

import vsl.lapack.lapack64

// Symmetric matrix
a := [
	[2.0, 1.0, 0.0],
	[1.0, 2.0, 1.0],
	[0.0, 1.0, 2.0],
]

// Compute eigenvalues and eigenvectors
// lapack64.dsyev('V', 'U', 3, mut a, mut eigenvalues)

General Matrices

For non-symmetric matrices, use different routines that handle complex eigenvalues.

Applications

  • Principal Component Analysis: Find principal directions
  • Vibration Analysis: Natural frequencies
  • Quantum Mechanics: Energy levels
  • Data Analysis: Dimensionality reduction

Example

// Compute eigenvalues of a matrix
// Visualize results
// Use eigenvectors for transformations

Next Steps