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A transformation x^'=Ax is unimodular if the determinant of the matrix A satisfies det(A)=+/-1. A necessary and sufficient condition that a linear transformation transform a ...

In an integral domain R, the decomposition of a nonzero noninvertible element a as a product of prime (or irreducible) factors a=p_1...p_n, (1) is unique if every other ...

In machine learning theory, the Vapnik-Chervonenkis dimension or VC-dimension of a concept class C is the cardinality of the largest set S which can be shattered by C. If ...

The vertex height of a vertex v in a rooted tree is the number of edges on the longest downward path between v and a tree leaf. The height of the root vertex of a rooted tree ...

The vertical line test is a graphical method of determining whether a curve in the plane represents the graph of a function by visually examining the number of intersections ...

The base-20 notational system for representing real numbers. The digits used to represent numbers using vigesimal notation are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F, ...

Vorobiev's theorem states that if F_l^2|F_k, then F_l|k, where F_n is a Fibonacci number and a|b means a divides b. The theorem was discovered by Vorobiev in 1942, but not ...

The Voronov-Neopryatnaya-Dergachev graphs are two graphs on 372 and 972 vertices which have unit-distance embeddings with all vertices on a sphere and chromatic number 5. The ...

There are at least two theorems known as Weierstrass's theorem. The first states that the only hypercomplex number systems with commutative multiplication and addition are ...

A totally ordered set (A,<=) is said to be well ordered (or have a well-founded order) iff every nonempty subset of A has a least element (Ciesielski 1997, p. 38; Moore 1982, ...