Length, area, and volume are all calculated differently in different orthogonal coordinate systems. The gradient of a function and the divergence and curl of vector fields, likewise, are calculated according to the orthogonal coordinates which the...

In matrix theory, a real orthogonal matrix is a square matrix Q whose transpose is its...

ABSTRACT The "breeding method" is a well-established and computationally inexpensive method for generating perturbations for ensemble integrations. One feature of bred vectors is that, although arbitrary initial perturbations generally converge toward the fastest growing directions, distinct bred vectors for global numerical weather prediction...

A statistical experiment limited by practical constraints may have to be conducted with less than the number of runs required in a regular orthogonal array. When this is anticipated, a design matrix which is a submatrix of an orthogonal array may be constructed in...