Cholesky Decomposition for Symmetric Matrices #ai #artificialintelligence #machinelearning #aiagent

Cholesky decomposition is a specialized matrix factorization technique applicable to symmetric, positive definite matrices. It decomposes a matrix into the product of a lower triangular matrix and its conjugate transpose. This method is more efficient than LU decomposition for this class of matrices, making it a preferred choice in various applications. In this block, we'll delve into the mathematical basis of Cholesky decomposition and demonstrate its implementation using NumPy's numpy.linalg.cholesky() function. We'll also explore its applications in optimization problems and numerical simulations, highlighting its significance in computational efficiency.