Mastering Python for Finance - Second Edition

The LU decomposition

The LU decomposition, or also known as lower-upper factorization, is one of the methods that solve square systems of linear equations. As its name implies, the LU factorization decomposes the A matrix into a product of two matrices: a lower triangular matrix, L, and an upper triangular matrix, U. The decomposition can be represented as follows:

Here, we can see a=l₁₁u₁₁, b=l₁₁u₁₂, and so on. A lower triangular matrix is a matrix that contains values in its lower triangle with the remaining upper triangle populated with ...