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MANOVA ("multiple analysis of variance") is a procedure for testing the equality of mean vectors of more than two populations. The technique is analogous to ANOVA for ...

Let x=(x_1,x_2,...,x_n) and y=(y_1,y_2,...,y_n) be nonincreasing sequences of real numbers. Then x majorizes y if, for each k=1, 2, ..., n, sum_(i=1)^kx_i>=sum_(i=1)^ky_i, ...

The natural norm induced by the L1-norm is called the maximum absolute column sum norm and is defined by ||A||_1=max_(j)sum_(i=1)^n|a_(ij)| for a matrix A. This matrix norm ...

Roughly speaking, the metric tensor g_(ij) is a function which tells how to compute the distance between any two points in a given space. Its components can be viewed as ...

An orthonormal set is a set of normalized orthogonal vectors or functions.

The pair group of a group G is the group that acts on the 2-subsets of {1,...,p} whose permutations are induced by G. Pair groups can be calculated using PairGroup[g] in the ...

Two lines in two-dimensional Euclidean space are said to be parallel if they do not intersect. In three-dimensional Euclidean space, parallel lines not only fail to ...

A real normed algebra, also called a composition algebra, is a multiplication * on R^n that respects the length of vectors, i.e., |x*y|=|x|*|y| for x,y in R^n. The only real ...

The rule which determines the orientation of the cross product u×v. The right-hand rule states that the orientation of the vectors' cross product is determined by placing u ...

The Sherman-Morrison formula is a formula that allows a perturbed matrix to be computed for a change to a given matrix A. If the change can be written in the form u tensor v ...