List of Matrices - Matrices Used in Statistics

Matrices Used in Statistics

The following matrices find their main application in statistics and probability theory.

• Bernoulli matrix — a square matrix with entries +1, −1, with equal probability of each.
• Centering matrix — a matrix which, when multiplied with a vector, has the same effect as subtracting the mean of the components of the vector from every component.
• Correlation matrix — a symmetric n×n matrix, formed by the pairwise correlation coefficients of several random variables.
• Covariance matrix — a symmetric n×n matrix, formed by the pairwise covariances of several random variables. Sometimes called a dispersion matrix.
• Dispersion matrix — another name for a covariance matrix.
• Doubly stochastic matrix — a non-negative matrix such that each row and each column sums to 1 (thus the matrix is both left stochastic and right stochastic)
• Fisher information matrix — a matrix representing the variance of the partial derivative, with respect to a parameter, of the log of the likelihood function of a random variable.
• Hat matrix - a square matrix used in statistics to relate fitted values to observed values.
• Precision matrix — a symmetric n×n matrix, formed by inverting the covariance matrix. Also called the information matrix.
• Stochastic matrix — a non-negative matrix describing a stochastic process. The sum of entries of any row is one.
• Transition matrix — a matrix representing the probabilities of conditions changing from one state to another in a Markov chain