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A number r is an nth root of unity if r^n=1 and a primitive nth root of unity if, in addition, n is the smallest integer of k=1, ..., n for which r^k=1.

A set function is a function whose domain is a collection of sets. In many instances in real analysis, a set function is a function which associates an affinely extended real ...

Let f_1(z), ..., f_m(z) for m>=1 be a set of E-functions that (1) form a solution of the system of differential equations y_k^'=q_(k0)+sum_(j=1)^mq_(kj)y_j for q_(kj) in C(z) ...

For every module M over a unit ring R, the tensor product functor - tensor _RM is a covariant functor from the category of R-modules to itself. It maps every R-module N to N ...

A square with side lengths 1. The unit square usually means the one with coordinates (0, 0), (1, 0), (1, 1), (0, 1) in the real plane, or 0, 1, 1+i, and i in the complex ...

The triangle DeltaM_AM_BM_C formed by joining the midpoints of the sides of a triangle DeltaABC. The medial triangle is sometimes also called the auxiliary triangle (Dixon ...

There are at least three theorems known as Jensen's theorem. The first states that, for a fixed vector v=(v_1,...,v_m), the function |v|_p=(sum_(i=1)^m|v_i|^p)^(1/p) is a ...

A 30-60-90 triangle is a right triangle having angles of 30 degrees, 60 degrees, and 90 degrees. For a 30-60-90 triangle with hypotenuse of length a, the legs have lengths b ...

The number of ways of picking k unordered outcomes from n possibilities. Also known as the binomial coefficient or choice number and read "n choose k," _nC_k=(n; ...

A method for finding a matrix inverse. To apply Gauss-Jordan elimination, operate on a matrix [A I]=[a_(11) ... a_(1n) 1 0 ... 0; a_(21) ... a_(2n) 0 1 ... 0; | ... | | | ... ...