Covariance matrix - Wikipedia

Abstraction: Square matrix encoding pairwise covariances of a random vector

Key points:

• Symmetric positive semi-definite square matrix; main diagonal contains variances, off-diagonal elements are covariances between variable pairs
• Inverse of the covariance matrix is the precision (concentration) matrix; encodes partial correlations
• Correlation matrix is a rescaled covariance matrix with diagonal elements equal to 1 and off-diagonals in [-1, 1]
• Enables PCA and the Karhunen-Loeve (whitening) transform by diagonalizing via orthogonal transformation
• Mahalanobis distance uses the pseudo-inverse covariance matrix as an inner product, measuring statistical "unlikelihood"
• Applied in portfolio theory (asset return diversification), evolution strategies (CMA-ES), and covariance mapping in spectroscopy

Connections: Covariance Matrix · Principal Component Analysis · Multivariate Statistics · Linear Algebra

Source: http://en.wikipedia.org/wiki/Covariance_matrix