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Consider a collection of diagonal matrices H_1,...,H_k, which span a subspace h. Then the ith eigenvalue, i.e., the ith entry along the diagonal, is a linear functional on h, ...

The primes nearest to the nonnegative integers n=0, 1, 2, ..., assigning ties to the smaller prime, are 2, 2, 2, 3, 3, 5, 5, 7, 7, 7, 11, 11, 11, 13, ... (OEIS A051697). If ...

The neighborhood graph of a given graph from a vertex v is the subgraph induced by the neighborhood of a graph from vertex v, most commonly including v itself. Such graphs ...

A nialpdrome is a number whose hexadecimal digits are in nonincreasing order. The first few are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 32, 33, 34, 48, 49, ...

The highest order power in a univariate polynomial is known as its order (or, more properly, its polynomial degree). For example, the polynomial ...

Given a hypergeometric or generalized hypergeometric function _pF_q(a_1,...,a_p;b_1,...,b_q;z), the corresponding regularized hypergeometric function is defined by where ...

Given the sum-of-factorials function Sigma(n)=sum_(k=1)^nk!, SW(p) is the smallest integer for p prime such that Sigma[SW(p)] is divisible by p. If pSigma(n) for all n<p, ...

A Z-number is a real number xi such that 0<=frac[(3/2)^kxi]<1/2 for all k=1, 2, ..., where frac(x) is the fractional part of x. Mahler (1968) showed that there is at most one ...

The converse of Pascal's theorem, which states that if the three pairs of opposite sides of (an irregular) hexagon meet at three collinear points, then the six vertices lie ...

The discriminant of the general conic section ax_1^2+bx_2^2+cx_3^2+2fx_2x_3+2gx_1x_3+2hx_1x_2=0 is defined as Delta=|a h g; h b f; g f c|=abc+2fgh-af^2-bg^2-ch^2. If b=a and ...