Linear Algebra

Eigenvalue

An eigenvalue is a scalar λ for which a non-zero vector v satisfies Av=λv.

Meaning

What Is Eigenvalue?

An eigenvalue is a scalar λ for which a non-zero vector v satisfies Av=λv.

An eigenvalue is a scalar λ for which a non-zero vector v satisfies Av=λv.

Examples

Examples of Eigenvalue

1If Av=2v, then 2 is an eigenvalue of A.
Understand

Formula and Key Points

Formula / rule
Av=λv
  • Know the definition and standard notation for Eigenvalue.
  • Be able to recognise or compute eigenvalue in a small example.
  • Connect the concept to nearby topics in the same subject before using it in larger CSE problems.
CSE Connection

Why This Matters in Computer Science

Used in computer graphics, machine learning, computer vision, signal processing, robotics and scientific computing. Used in PageRank, stability analysis, PCA and spectral graph methods.

FAQ

Eigenvalue: Frequently Asked Questions

What is Eigenvalue?

An eigenvalue is a scalar λ for which a non-zero vector v satisfies Av=λv.

Why is Eigenvalue useful in computer science?

Used in computer graphics, machine learning, computer vision, signal processing, robotics and scientific computing. Used in PageRank, stability analysis, PCA and spectral graph methods.