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A mathematical statement of the equivalence of two quantities. The equality "A is equal to B" is written A=B.

An operator A^~ such that A^~^2=A^~ or an element of an algebra x such that x^2=x.

The double covering group of the (linear) symplectic group.

A quantity which is either 0 (zero) or positive, i.e., >=0.

An integer that is either 0 or negative, i.e., a member of the set {0} union Z^-, where Z-- denotes the negative integers.

p^~=|phi_i(x)><phi_i(t)| (1) p^~sum_(j)c_j|phi_j(t)>=c_i|phi_i(x)> (2) sum_(i)|phi_i(x)><phi_i(x)|=1. (3)

The words random and stochastic are synonymous.

The word "spectrum" confusingly has a number of unrelated meanings in various branches of mathematics.

The robustness of a given outcome to small changes in initial conditions or small random fluctuations. Chaos is an example of a process which is not stable.

The tangent plane to a surface at a point p is the tangent space at p (after translating to the origin). The elements of the tangent space are called tangent vectors, and ...