What are Eigenvalues and Eigenvectors?
Eigenvalues and eigenvectors are fundamental concepts in linear algebra, crucial for understanding systems of linear equations, transformations, and much more!
The Mathematics Behind It
For a square matrix A, if there exists a scalar λ and a nonzero vector v such that Av = λv, then λ is called an eigenvalue and v is the corresponding eigenvector.
Eigenvalues can be complex numbers, but in many practical applications, they are real numbers.
Applications of Eigenvalues and Eigenvectors
- Principal Component Analysis in data science and statistics.
- Stability analysis of systems in engineering.
- Quantum mechanics and vibration analysis in physics.