# Wishart distribution

(30 minutes to learn)

## Summary

The Wishart distribution is a distribution over positive semidefinite matrices. It is most often used as the conjugate prior for the precision matrix of a multivariate Gaussian.

## Context

This concept has the prerequisites:

- gamma distribution (The Wishart distribution is a multivariate generalization of the gamma distribution.)
- positive definite matrices (The Wishart distribution is a distribution over positive definite matrices.)
- expectation and variance (We would like to derive the mean of the distribution.)
- determinant (The probability density function includes a determinant.)
- matrix inverse (The probability density function includes a matrix inverse.)

## Core resources (read/watch one of the following)

## -Paid-

→ Machine Learning: a Probabilistic Perspective

A very comprehensive graudate-level machine learning textbook.

Location:
Section 4.5, pages 125-127

## See also

- sampling from a Wishart distribution
- math tricks for Wishart distributions