Length Vector Rotation Matrix Constraints | Preserve A

Thread starter mind game
Start date Oct 2, 2005
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Lenght Vector

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To preserve the length of vector A during rotation in three-dimensional space, the rotation matrix R must satisfy the condition that the transpose of R multiplied by R equals the identity matrix (R^T R = I). This ensures that the transformation does not alter the magnitude of vector A. The discussion emphasizes the importance of matrix algebra in deriving these constraints. Participants are encouraged to explore the mathematical properties and implications of rotation matrices further. Understanding these constraints is crucial for applications involving vector transformations in physics and engineering.

Oct 2, 2005

mind game

what constraints must the elements of three dimensional rotation matrix satisfy in order to preserve length of vector A

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Oct 2, 2005

robphy

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Here's a start:
your question expressed symbolically...
{\vec A'}^\top\vec A'=(R\vec A)^\top(R\vec A)=\vec A^\top\vec A

So, what must R satisfy? Can you do matrix algebra?

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