LU Decomposition - An Example Calculation

Veröffentlicht am: 30 Dezember 2019
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🌙 There is also a dark mode version of this video:    • LU Decomposition - An Example Calculation ...
🔆 There is also a bright mode version of this video:    • LU Decomposition - An Example Calculation

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There is a whole video series about Linear Algebra you should watch to understand the importance of the subject. I hope that it will help everyone who wants to learn about it. You find it: https://tbsom.de/s/la and https://tbsom.de/s/ala

This video is about the LU decomposition for square matrices. I show the algorithm with the help of an example.

I hope that it will help everyone who wants to learn about it. We discuss the whole Gauss algorithm for the LU decomposition. For any questions, please leave a comment or come to the community forum of the Bright Side of Mathematics: https://tbsom.de/s/community

The name stands for lower–upper (LU) decomposition or factorization because we have lower triangular matrix and an upper triangular matrix involved. This example is for a square matrix where no row exchanges are needed. The more general case is called PLU-decomposition and I have a video about this:    • PLU decomposition - An Example

0:00 Introduction
0:33 Start Example
1:45 First step
2:41 Eliminating the first column
5:35 Eliminating the second column
7:10 Eliminating the third column
7:38 Result of the LU decomposition

#LinearAlgebra
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#Derivatives

I hope that this helps students, pupils and others. Have fun!

(This explanation fits to lectures for students in their first and second year of study: Mathematics for physicists, Mathematics for the natural science, Mathematics for engineers and so on)

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