Undergrad Matrix Decomposition Explained: Simple Illustration

[mohammed El-Kady]

Can anyone illustrate for me matrix decomposition in a simple way?

 

[berkeman]

https://en.wikipedia.org/wiki/Matrix_decomposition

 

[Ray Vickson]

Can anyone illustrate for me matrix decomposition in a simple way?

There are several types: LU-decomposition, QR- decomposition, and probably others.

You need to be more specific, and your question needs more focus. Are you interested in (1) WHY perform decompositition; or (2) HOW to perform decompostition?

 

[WWGD]

SVD is pretty popular : https://duckduckgo.com/?q=singular+value+decomposition&t=h_&ia=web

Part of the idea is to simplify the whole by breaking it into components.

 

[mohammed El-Kady]

thank you for your responses, while i study elasticity it have been mentioned that deformation tensor is stretch and rotation tensor and the proof by using matrix decomposition, I've no idea about the type of decomp.

 

[fresh_42]

thank you for your responses, while i study elasticity it have been mentioned that deformation tensor is stretch and rotation tensor and the proof by using matrix decomposition, I've no idea about the type of decomp.

It's the decomposition into a orthogonal rotation $U$ and a symmetric positive definite stretching $P$, see the polar decomposition https://en.wikipedia.org/wiki/Polar_decomposition

 

[mohammed El-Kady]

It's the decomposition into a orthogonal rotation $U$ and a symmetric positive definite stretching $P$, see the polar decomposition https://en.wikipedia.org/wiki/Polar_decomposition

thank you too much, its helpful and valuable and easy

 

[WWGD]

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