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A plane path on a set of equally spaced lattice points, starting at the origin, where the first step is one unit to the north or south, the second step is two units to the ...

A polygon whose vertices are points of a point lattice. Regular lattice n-gons exists only for n=3, 4, and 6 (Schoenberg 1937, Klamkin and Chrestenson 1963, Maehara 1993). A ...

Matrix diagonalization is the process of taking a square matrix and converting it into a special type of matrix--a so-called diagonal matrix--that shares the same fundamental ...

The minimal polynomial of a matrix A is the monic polynomial in A of smallest degree n such that p(A)=sum_(i=0)^nc_iA^i=0. (1) The minimal polynomial divides any polynomial q ...

Modular arithmetic is the arithmetic of congruences, sometimes known informally as "clock arithmetic." In modular arithmetic, numbers "wrap around" upon reaching a given ...

Reciprocation is an incidence-preserving transformation in which points are transformed into their polars. A projective geometry-like duality principle holds for ...

The 27 real or imaginary lines which lie on the general cubic surface and the 45 triple tangent planes to the surface. All are related to the 28 bitangents of the general ...

The transformation S[{a_n}_(n=0)^N] of a sequence {a_n}_(n=0)^N into a sequence {b_n}_(n=0)^N by the formula b_n=sum_(k=0)^NS(n,k)a_k, (1) where S(n,k) is a Stirling number ...

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 matrix is a concise and useful way of uniquely representing and working with linear transformations. In particular, every linear transformation can be represented by a ...