Mary Layne Boas, Mathematical Methods in the Physical Sciences 3rd edition (Wiley, 2005)
Chapter 3. Linear Algebra
Section 7. Linear Combinations, Linear Functions, Linear Operators
Let the matrix represent an active transformation of vectors in the (x, y) plane (axes fixed, vectors rotated or reflected). Show that the matrix is orthogonal, find its determinant, and find the rotation angle, or find the line of reflection.
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It's easy, simple, straightforward, effortless, uncomplicated, undemanding, not difficult.
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