A covariance matrix is a square table that shows the covariances between multiple variables. Each element in the matrix represents how much two variables vary together. The diagonal elements are the variances of each variable, while the off-diagonal elements are the covariances between pairs of variables. Covariance matrices are used in multivariate statistics, such as in principal component analysis, factor analysis, and portfolio risk analysis.
For example, a covariance matrix for three stock returns might show how the returns of each pair of stocks move in relation to each other. If Stock A and Stock B have a high positive covariance, they tend to rise and fall together.
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