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Show that the orthogonality condition is preserved under an orthogonal transformation.

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Part i) Show that if u & v are orthogonal, then the transformed vectors U = Au & V = Av under the linear (orthogonal) transformation (characterised by the orthogonal matrix A) are themselves orthogonal. I think this can be done using pythagoras theorem but am not sure how to begin, please help!

Part ii) shSw that the orthogonal transformation preserves the dot product i.e Au dot Av = u dot v. Hence or otherwise show that the angles between 2 vectors are preserved under the orthogonal transformation

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With good explanations and diagrams, the problems are solved. Orthogonality conditions preserved under orthogonal transforms are determined.

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