In linear algebra, the Cholesky decomposition or Cholesky triangle is a decomposition of a Hermitian, positive-definite matrix into the product of a lower triangular matrix and its conjugate transpose. It was discovered by André-Louis Cholesky for real matrices. When it is applicable, the Cholesky decomposition is roughly twice as efficient as the LU decomposition for solving systems of linear equations. In a loose, metaphorical sense, this can be thought of as the matrix analogue of taking the square root of a number.
Read more about Cholesky Decomposition: Statement, Applications, Computing The Cholesky Decomposition, Proof For Positive Semi-definite Matrices, Generalization, Updating The Decomposition