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A projection matrix P is an n×n square matrix that gives a vector space projection from R^n to a subspace W. The columns of P are the projections of the standard basis ...

A finite simple connected graph G is quadratically embeddable if its quadratic embedding constant QEC(G) is nonpositive, i.e., QEC(G)<=0. A graph being quadratically ...

A sequence of n-tuples that fills n-space more uniformly than uncorrelated random points, sometimes also called a low-discrepancy sequence. Although the ordinary uniform ...

The mathematical study of combinatorial objects in which a certain degree of order must occur as the scale of the object becomes large. Ramsey theory is named after Frank ...

A rational amicable pair consists of two integers a and b for which the divisor functions are equal and are of the form sigma(a)=sigma(b)=(P(a,b))/(Q(a,b))=R(a,b), (1) where ...

The Riemann integral is the definite integral normally encountered in calculus texts and used by physicists and engineers. Other types of integrals exist (e.g., the Lebesgue ...

There are a couple of versions of this theorem. Basically, it says that any bounded linear functional T on the space of compactly supported continuous functions on X is the ...

A round number is a number that is the product of a considerable number of comparatively small factors (Hardy 1999, p. 48). Round numbers are very rare. As Hardy (1999, p. ...

The SI prefixes are the 20 power-of-10 prefixes specified by the Bureau International des Poids et Mesures (BIPM) for use in the International System of Units (SI). They are ...

The sample variance m_2 (commonly written s^2 or sometimes s_N^2) is the second sample central moment and is defined by m_2=1/Nsum_(i=1)^N(x_i-m)^2, (1) where m=x^_ the ...