Epsilons, no. 3: The LU decomposition

How determinants and matrix inverses are calculated

Matrix factorizations are the pinnacle results of linear algebra.

Factorizations enable both theoretical and numerical results, ranging from inverting matrices to dimensionality reduction of feature-rich datasets. Check out my Linear Algebra for Machine Learning book if you don’t believe me.

In this mini-series within the Epsilon series, we’ll take a quick look at four of the most important matrix factorization methods:

• the LU decomposition,

• the QR decomposition,

• the spectral theorem,

• and the Singular Value Decomposition.

Let’s start with the first one: the LU decomposition, that is, the factorization of a matrix into the product of an upper and lower triangular one.

Why is such a decomposition useful? There are two main applications:

• computing determinants,

• and inverting matrices.

For instance, check out how the LU decomposition simp…