If Matrix is Positive Definite
Matrix Algebra DS practice problem on Onlearn.
Difficulty: medium.
Topics: Understanding Positive Definite Matrices in Linear Algebra, Cholesky Factorization, Principal Minors, Spectral Theorem, Floating-point Precision, Matrix Transposition, Linear Algebra, Matrix Theory, Numerical Analysis, Optimization Foundations, Computational Statistics, Symmetric Matrices, Decomposition Methods, Quadratic Forms, Determinants and Minors, Eigenvalue Theory.
Write a function that determines whether a given square matrix is positive definite. A matrix A is positive definite if it is symmetric (A = A^T) and x^T A x 0 for all non zero vectors x. You should check for symmetry and use the Cholesky decomposition method to verify positive definiteness. Return True if positive definite, False otherwise.