Since I can't comment, I wish to add this: the Cholesky decomposition (or its variant, LDL T, L a unit lower triangular matrix and D a diagonal matrix) can be used to verify if a symmetric matrix is positive/negative definite: if it is positive definite, the elements of D are all positive, and the Cholesky decomposition will finish successfully without taking the square root of a negative number.
chosen, the two special linear transformations 0 and I are always identiﬁed with the null matrix and the identity matrix, respectively. Deﬁnition 3.4 (Matrix Multiplication) Given two matrices A : m × n and B : n×p, the matrix product C = AB (in this order) is an m×p matrix with typical elements cij = Xn k=1 aikbkj
A determinant is a real number or a scalar value associated with every square matrix. Let A be the symmetric matrix, and the determinant is denoted as “ det A” or |A|. Here, it refers to the determinant of the matrix A. After some linear transformations specified by the matrix, the determinant of the symmetric matrix is determined.