a type (2,0) tensor that is initially symmetric and the transformed tensor remains symmetric

A tensor's symmetry is a fundamental property that is preserved under coordinate transformations. The demo visually confirms that even as the tensor's individual components change and the coordinate system rotates, the relationship between the off-diagonal elements remains symmetrical, proving that if $T^{a b}=T^{b a}$, then $T^{\prime a^{\prime} b^{\prime}}=T^{\prime b^{\prime} a^{\prime}}$. This shows that symmetry is an intrinsic characteristic of the tensor itself, not just a feature of how it's represented in a particular coordinate system.

🎬Demo

https://youtu.be/0BEsZtG95M8

🏗️Structural clarification of Poof and Derivation

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🗒️Downloadable Files - Recursive updates

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Copyright Notice

All content and images on this page are the property of Sayako Dean, unless otherwise stated. They are protected by United States and international copyright laws. Any unauthorized use, reproduction, or distribution is strictly prohibited. For permission requests, please contact [email protected]

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