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Covariance matrix

In probability theory and statistics, a covariance matrix (also known as auto-covariance matrix, dispersion matrix, variance matrix, or variance–covariance matrix) is a square matrix giving the covariance between each pair of elements of a given random vector.

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Overview

Definition

Properties

Partial covariance matrix

Standard deviation matrix

Covariance matrix as a parameter of a distribution

Covariance matrix as a linear operator

Admissibility

Complex random vectors

Estimation

Applications

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Covariance matrix

Nodes86
Edges85
Triples93
Avg. degree1.98
Density0.023256
Components1

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Covariance matrix

Top relations

related to Further reading · 14
Covariance matrix → Covariance, Covariance Matrix Explained With, EMS Press, Encyclopedia, Eric, ISBN, Kampen, Mathematics, MathWorld, New York, North-Holland, Pictures, Stochastic, Weisstein
related to Conflicting nomenclatures and notations · 9
Covariance matrix → An Introduction, Both, Its Applications, Nomenclatures, Others, Probability Theory, Some, The, William Feller
has application · 8
Covariance matrix → From, Karhunen, KL-transform, Loève, PCA, Rayleigh, The, This
related to Covariance mapping · 8
Covariance matrix → Bessel's, In, Matlab, Statistically, The, Using, When, XY
related to Block matrices · 6
Covariance matrix → Sigma, The, XX, XY, YX, YY
related to Covariance matrix as a linear operator · 6
Covariance matrix → Applied, Mahalanobis, Sigma, Similarly, The, Treated
related to Partial covariance matrix · 6
Covariance matrix → If, Often, The, They, This, XY
related to Use in optimization · 5
Covariance matrix → Hessian, Intuitively, Randomized Search Heuristics, The, There
related to Complex random vectors · 4
Covariance matrix → Hermitian, If, In, The
related to Pseudo-covariance matrix · 4
Covariance matrix → For, Hermitian, In, Its

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Important terminology

covariance matrix displaystyle mathbf operatorname random mathsf cov vector variance sigma variables symmetric left right mu boldsymbol correlations also var

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Covariance matrixis amatrix of Pearson product-moment correlation coefficients between each of the random variables in the random vector X0.90text
Covariance matrixis aHermitian matrix0.90text
Covariance matrixis auseful tool in many different areas0.90text
Matlab.Figinstance ofwhich bypasses the requirement to invert a matrix and is available in some computational packages0.80text
Covariance matrixhas applicationThe0.60section
Covariance matrixhas applicationFrom0.60section
Covariance matrixhas applicationRayleigh0.60section
Covariance matrixhas applicationThis0.60section
Covariance matrixhas applicationPCA0.60section
Covariance matrixhas applicationKarhunen0.60section
Covariance matrixhas applicationLoève0.60section
Covariance matrixhas applicationKL-transform0.60section

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