Thornton & Marion, Classical Dynamics of Particles and Systems, 5th Edition
Chapter 1. Matrices, Vectors, and Vector Calculus
Problem 05. The determinant of the transformation matrix
The problem asks you to
- show that $latex |\\bold{\\lambda}|^2 = 1$
This problem assumes
- The transformation matrix $latex \\bold{\\lambda}$ to be a two-dimensional orthogonal matrix.
You should know about
- Calculation of a determinant
- Properties of the orthogonal transformation matrix
Solution
Since the transformation matrix $latex \\bold{\\lambda}$ is
So
From Equation (1.13), which is the orthogonality condition,
Therefore,
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