Lemma
DeepChange of variables
Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §14.4 Cylindrical and Spherical Coordinates, #35 · Multivariable Calculus · Change of variables

A pure stretching has …, …, and

A pure stretching has , , and . Find the 3 by 3 matrix and its determinant . What is special about the box in this case?

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §14.4 Cylindrical and Spherical Coordinates, #35

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