Implementing a decomposition method

For this recipe, we will implement a matrix decomposition method for linear regression. Specifically, we will use Cholesky decomposition, for which relevant functions exist in TensorFlow.

Getting ready

Implementing the inverse methods from the previous recipe can be numerically inefficient in most cases, especially when the matrices get very large. Another approach is to decompose the A matrix and perform matrix operations on the decompositions instead. One such approach is to use the built-in Cholesky decomposition method in TensorFlow.

One reason people are so interested in decomposing a matrix into more matrices is that the resultant matrices will have assured properties that allow us...