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A standard basis, also called a natural basis, is a special orthonormal vector basis in which each basis vector has a single nonzero entry with value 1. In n-dimensional ...

The Steenrod algebra has to do with the cohomology operations in singular cohomology with integer mod 2 coefficients. For every n in Z and i in {0,1,2,3,...} there are ...

Triangle picking is the process of picking triangles at random within a given shape in the plane, in space, or in a higher dimension. The most natural definition of a random ...

Given an n-dimensional vector x=[x_1; x_2; |; x_n], (1) a general vector norm |x|, sometimes written with a double bar as ||x||, is a nonnegative norm defined such that 1. ...

The matrix product of a square set of data d and a matrix of basis vectors consisting of Walsh functions. By taking advantage of the nested structure of the natural ordering ...

The exponential function has two different natural q-extensions, denoted e_q(z) and E_q(z). They are defined by e_q(z) = sum_(n=0)^(infty)(z^n)/((q;q)_n) (1) = _1phi_0[0; ...

A (-1,0,1)-matrix is a matrix whose elements consist only of the numbers -1, 0, or 1. The number of distinct (-1,0,1)-n×n matrices (counting row and column permutations, the ...

An addition-multiplication square is a square of integers that is simultaneously a magic square and multiplication magic square. In 1955, Horner found a square of order eight ...

The Fibonacci number F_(n+1) gives the number of ways for 2×1 dominoes to cover a 2×n checkerboard, as illustrated in the diagrams above (Dickau). The numbers of domino ...

The Goddard-Henning graph, illustrated above in several embeddings, is the 9-node planar graph of graph diameter 2 having domination number gamma=3. It was first constructed ...