# I Matrix decomposition

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

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#### Ray Vickson

Homework Helper
Dearly Missed
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

Gold Member

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

Mentor
2018 Award
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

#### WWGD

Gold Member
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