Show that the orthogonality condition is preserved under an orthogonal transformation.
Not what you're looking for? Search our solutions OR ask your own Custom question.
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
© BrainMass Inc. brainmass.com December 15, 2022, 5:54 pm ad1c9bdddfhttps://brainmass.com/physics/scalar-and-vector-operations/orthogonality-condition-preserved-under-orthogonal-transform-112062
Solution Summary
With good explanations and diagrams, the problems are solved. Orthogonality conditions preserved under orthogonal transforms are determined.
$2.49