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The Schur decomposition of a complex square matrix A is a matrix decomposition of the form Q^(H)AQ=T=D+N, (1) where Q is a unitary matrix, Q^(H) is its conjugate transpose, ...

Symmetry operations include the improper rotation, inversion operation, mirror plane, and rotation. Together, these operations create 32 crystal classes corresponding to the ...

A straight line is tangent to a given curve f(x) at a point x_0 on the curve if the line passes through the point (x_0,f(x_0)) on the curve and has slope f^'(x_0), where ...

A Tucker hexagon is a hexagon inscribed in a reference triangle that has sides which are alternately parallel and antiparallel to the corresponding sides of the triangle. ...

Consider expressions built up from variables and constants using function symbols. If v_1, ..., v_n are variables and t_1, ..., t_n are expressions, then a set of mappings ...

A particle P is said to be undergoing uniform circular motion if its radius vector in appropriate coordinates has the form (x(t),y(t),0), where x(t) = Rcos(omegat) (1) y(t) = ...

Let A be a unital C^*-algebra. An element u in A is called unitary if u^*u=uu^*=1. For example, for each self-adjoint element a in A, the element ...

Let a vault consist of two equal half-cylinders of radius r which intersect at right angles so that the lines of their intersections (the "groins") terminate in the ...

Let X_1, ..., X_N be a sequence of independent observations of a random variable X, and let the number of observations N itself be chosen at random. Then Wald's equation ...

The weighted mean of a discrete set of numbers {x_1,x_2,...,x_n} with weights {w_1,w_2,...,w_n} is given by <x>=sum_(i=1)^nw_ix_i, (1) where each weight w_i is a nonnegative ...