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What is Cross Product and Orthogonal Transformations about?

1) Orthogonal transformations preserve the cross product in R3. Specifically, for any orthogonal matrix A and vectors x, y in R3, the cross product of Ax and Ay is equal to the determinant of A multiplied by the cross product of x and y. 2) This follows from the property that orthogonal matrices preserve dot products. The proof uses a lemma stating that two vectors are equal if and only if they have equal dot products with all other vectors. 3) The proof shows that the dot product of Ax × Ay with any v

Author

Misbah Shafique

Language

EN