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Working with Rotational Matrices

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R is a 3x3 matrix. What property is required of R for it to be an orthogonal matrix. and (I:-) a rotation matrix? Write down the matrix that effects a rotation by angle theta about the y-axis.

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Solution Summary

This provides an example of how to work with rotational matrices in an attachment. The matrix effects on rotation by angle theta about the y-axis is determined.

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(a) A 3 x 3 matrix R is an orthogonal matrix is RRt = RtR = I, i.e., its transpose is its inverse.
(b) A 3 x 3 matrix R is a rotation matrix if in addition to being an orthogonal matrix, its determinant is equal to +1.
i.e., RRt = RtR = I and det(R) = 1
The 3 x 3 rotation matrix is:

b = M.a
Premultiplying ...

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