# What Is The Covariance Of A Matrix

This post categorized under Vector and posted on June 11th, 2018.

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In probability theory and statistics a covariance matrix (also known as dispersion matrix or variancecovariance matrix) is a matrix whose element in the i j position is the covariance between the i-th and j-th elements of a random vector.In probability theory and statistics covariance is a measure of the joint variability of two random variables. If the greater values of one variable mainly correspond with the greater values of the other variable and the same holds for the lesser values (i.e. the variables tend to show similar behavior) the covariance is positive.These directions are actually the directions in which the data varies the most and are defined by the covariance matrix. The covariance matrix can be considered as a matrix that linearly transformed some original data to obtain the currently observed data.

Improved Estimation of the Covariance Matrix of Stock Returns With an Application to Portfolio Selection Olivier Ledoit and Michael Wolf AbstractIf True the support of the robust location and the covariance estimates is computed and a covariance estimate is recomputed from it without centering the data.

2x2 Matrix. OK how do we calculate the inverse Well for a 2x2 matrix the inverse is In other words swap the positions of a and d put negatives in front of b and c and divide everything by the determinant (ad-bc).Shrinkage covariance estimation LedoitWolf vs OAS and max-likelihood. When working with covariance estimation the usual approach is to use a maximum likelihood estimator such as the sklearn.covariance.EmpiricalCovariance.