What is p-matrix?

P-matrix stands for a positive definite matrix, which is a square matrix having all its eigenvalues positive. A matrix is called positive-definite if for any nonzero column vector x, the scalar x'Ax is positive, where A is the matrix and x' represents the transpose of x. In other words, p-matrix is a type of matrix in which all the diagonal elements are positive, and all the off-diagonal elements are negative or zero. P-matrix is used in various fields such as optimization, statistics, and physics. It is often used in the analysis of systems of linear equations, where it provides information about the solvability and stability of the system. Additionally, p-matrix is important in structural engineering, where it is used to analyze the stability of structures and in numerical analysis, where it is used to design efficient algorithms for solving systems of linear equations.