LU factorization

Summary

LU factorizable

• is a unit lower triangular matrix
• is a upper triangular matrix

Algorithm for solving linear systems via LU factorisation

No LU factorization

• if any of its leading principal minors are 0

Concept

Rationale for LU factorization

Unit lower triangular matrix

Product of 2 unit lower triangular matrix

Application

General solution by LU factorization

Non LU factorisiable matrix

Extra

Octave

# LU factorization
[L U] = lu(A)
y = inv(L) * b
x = inv(U) * y