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Let there be three polynomials a(x), b(x), and c(x) with no common factors such that a(x)+b(x)=c(x). Then the number of distinct roots of the three polynomials is one or more ...

The product C of two matrices A and B is defined as c_(ik)=a_(ij)b_(jk), (1) where j is summed over for all possible values of i and k and the notation above uses the ...

A quotient-difference table is a triangular array of numbers constructed by drawing a sequence of n numbers in a horizontal row and placing a 1 above each. An additional "1" ...

A symmetric matrix is a square matrix that satisfies A^(T)=A, (1) where A^(T) denotes the transpose, so a_(ij)=a_(ji). This also implies A^(-1)A^(T)=I, (2) where I is the ...

For every even dimension 2n, the symplectic group Sp(2n) is the group of 2n×2n matrices which preserve a nondegenerate antisymmetric bilinear form omega, i.e., a symplectic ...

A transition function describes the difference in the way an object is described in two separate, overlapping coordinate charts, where the description of the same set may ...

The Euclidean algorithm, also called Euclid's algorithm, is an algorithm for finding the greatest common divisor of two numbers a and b. The algorithm can also be defined for ...

Given a group of n men arranged in a circle under the edict that every mth man will be executed going around the circle until only one remains, find the position L(n,m) in ...

If X and Y are independent variates and X+Y is a normal distribution, then both X and Y must have normal distributions. This was proved by Cramér in 1936.

The Grassmannian Gr(n,k) is the set of k-dimensional subspaces in an n-dimensional vector space. For example, the set of lines Gr(n+1,1) is projective space. The real ...