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Show that orthogonal transformation preserves dot product

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Reference no: EM13965396

1. 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!

2. Show 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.

Reference no: EM13965396

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