A Positive Definite Matrix is a special type of square matrix that has important properties in mathematics and statistics. It is defined such that for any non-zero vector x, the product x^T * A * x is always greater than zero, where A is the matrix in question. This means that the matrix is always "positive" in a certain sense, indicating that it represents a form of energy or distance. These matrices are commonly used in various fields, including machine learning, optimization, and statistics. For example, the covariance matrix in statistics is often positive definite, ensuring that the variances are non-negative and that the relationships between variables are well-defined.