What is LU Factorization (also known as LU Decomposition) and how do we perform it on a matrix? LU Factorization essentially allows us to solve a matrix a single time and apply the scaling factors to any possible constant vector that the matrix could equal. Therefore, LU Decomposition can save us large amounts of time it can also allow us to easily find the determinant of the matrix!
The following timeline is meant to aid your understanding of LU factorization:
0:00 Introduction.
0:18 General formula for LU factorization.
0:27 Why do we need LU decomposition?
0:44 The purpose of LU factorization.
1:07 The meaning of LU factorization.
1:40 How LU factorization works.
2:43 LU factorization example.
4:55 Easily find determinant of any matrix with LU factorization.
5:30 Outro
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This video is part of our Numerical Methods course. Numerical methods is about solving math problems through approximating the solution of problems that would be difficult or impossible to solve analytically. In this playlist we will cover topics such as solving systems of linear equations, solving systems of non-linear equations, numerical integration, numerical derivatives, etc..
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