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A piecewise function is a function that is defined on a sequence of intervals. A common example is the absolute value, |x|={-x for x<0; 0 for x=0; x for x>0. (1) Piecewise ...

Plancherel's theorem states that the integral of the squared modulus of a function is equal to the integral of the squared modulus of its spectrum. It corresponds to ...

A theory of constructing initial conditions that provides safe convergence of a numerical root-finding algorithm for an equation f(z)=0. Point estimation theory treats ...

A point group is a group of symmetry operations which all leave at least one point unmoved. Although an isolated object may have an arbitrary Schönflies symbol, the ...

The diagonal of a polyhedron is any line segment connecting two nonadjacent vertices of the polyhedron. Any polyhedron having no diagonals must have a skeleton which is a ...

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

A pseudoinverse is a matrix inverse-like object that may be defined for a complex matrix, even if it is not necessarily square. For any given complex matrix, it is possible ...

Given a matrix A, its QR-decomposition is a matrix decomposition of the form A=QR, where R is an upper triangular matrix and Q is an orthogonal matrix, i.e., one satisfying ...

The Racah V-coefficients are written V(j_1j_2j;m_1m_2m) (1) and are sometimes expressed using the related Clebsch-Gordan coefficients C_(m_1m_2)^j=(j_1j_2m_1m_2|j_1j_2jm), ...

The Racah W-coefficients, sometimes simply called the Racah coefficients (Shore and Menzel 1968, p. 279), are quantities introduced by Racah (1942) that are related to the ...