Linear Algebra › Section B · Matrix algebra › Topic B.5
Matrix factorizations and LU
Factoring a number such as 12 = 3 × 4 reveals its structure. Factoring a matrix does the same, and the LU factorisation, which records the work of row reduction, is how computers actually solve most square linear systems.
In this topic
- Why factor a matrix?
- What A = LU means
- Solving with the two factors
- Finding L and U
- Worked example: factoring a 3 × 3 matrix
- Worked example: solving with the factors
- Counting the cost
- When rows must be swapped
- Common mistakes to avoid
- Key takeaways
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