1. The Wishart distribution is a probability distribution that generalizes the chi-squared distribution to multiple dimensions. 2. It is used to describe the distribution of sample covariance matrices drawn from a multivariate normal population. 3. Formally, if $X$ is a $p \times n$ matrix whose columns are independent $p$-dimensional Gaussian vectors with mean zero and covariance matrix $\Sigma$, then the matrix $S = XX^T$ follows a Wishart distribution with parameters $\Sigma$ and $n$ degrees of freedom. 4. The probability density function (pdf) of the Wishart distribution for a positive-definite matrix $S$ is given by: $$ f(S) = \frac{|S|^{(n-p-1)/2} e^{-\frac{1}{2} \mathrm{tr}(\Sigma^{-1} S)}}{2^{np/2} |\Sigma|^{n/2} \Gamma_p(\frac{n}{2})} $$ where $|S|$ is the determinant of $S$, $\mathrm{tr}$ is the trace operator, and $\Gamma_p$ is the multivariate gamma function. 5. The Wishart distribution is important in multivariate statistics, especially in estimation of covariance matrices and hypothesis testing.