# Eigenvalue

*Math & Statistics — Finicade finance glossary*

An eigenvector is a direction a matrix stretches without rotating, and the eigenvalue is how much it stretches. For a covariance matrix, the eigenvectors are the independent directions of risk and the eigenvalues are how much variance sits in each. That's why a negative eigenvalue is a red flag: it means the correlation matrix is inconsistent and implies a portfolio with negative variance.

**Also known as:** eigenvector, eigenvalues and eigenvectors, spectral decomposition

**Related terms:** [Matrix](https://finicade.com/glossary/matrix), [Principal Component Analysis](https://finicade.com/glossary/principal-component-analysis), [Covariance](https://finicade.com/glossary/covariance), [Cholesky Decomposition](https://finicade.com/glossary/cholesky-decomposition), [Vector and Matrix](https://finicade.com/glossary/vector)

Source: https://finicade.com/glossary/eigenvalue