LDL Transpose (LDLT) Decomposition - Computational Linear Algebra
Channel: Nick Space Cowboy
Date: 2022-04-17

This video is about the LDL transpose decomposition in linear algebra.

Github: https://github.com/nkphysics/Computational-Linear-Algebra-/tree/master/Unit1/8_LDLT
Gitlab: https://gitlab.com/n_space_cowboy/computational-linear-algebra/-/tree/master/8_LDLT.

In this video we cover a higher level variant of the LDV matrix decomposition  called the LDLT or LDL transpose matrix decomposition. The LDLT or LDL transpose matrix decomposition uses our working knowledge of the Choleksy decomposition to decompose a matrix into 3 matrices, where we only need to track two of them since the lower triangular matrix can be transposed and fill the place of the V matrix in the LDV matrix decomposition. In this video we perform the LDL Transpose decomposition in the python programming language. The LDL transpose matrix decomposition, being a higher level matrix decomposition, only is allowed to be performed when certain initial conditions are met. In this case since we use the Cholesky matrix decomposition we need the matrix to be positive definite in order to perform the LDL transpose matrix decomposition.