Cholesky Decomposition
Decomposition & Spectral Methods DS practice problem on Onlearn.
Difficulty: medium.
Topics: Understanding Cholesky Decomposition for Positive Definite Matrices, Symmetry condition, Square root extraction in matrices, Inner product summation, Outer product elimination, Floating point precision errors, Linear Algebra, Numerical Analysis, Matrix Theory, Computational Statistics, Optimization Theory, Positive Definite Matrices, Triangular Decomposition, Quadratic Forms, Computational Complexity, Numerical Stability.
Implement the Cholesky decomposition of a symmetric, positive definite matrix A into a lower triangular matrix L such that A = LL^T. The function should take a 2D list (matrix) as input and return the 2D list representing L.