Linear Algebra - Prove that the rotation matrix A_ϴ(theta) is an orthogonal matrix.?
Linear Algebra - Prove that the rotation matrix A_ϴ(theta) is an orthogonal matrix. Show details and step by step proof
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If A_Θ = [ cos Θ....- sin Θ]
.............[ sin Θ .....cos Θ] then it is obvious since cos² Θ + sin² Θ = 1 and
- cos Θ sin Θ + cos Θ sinΘ = 0...do you know the conditions for orthogonality of a matrix ?