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The ratio C of the largest to smallest singular value in the singular value decomposition of a matrix. The base-b logarithm of C is an estimate of how many base-b digits are ...

A dependent variable is a variable whose value depends on the values of one or more other independent variables. This notion comes up regularly in a variety of contexts. In ...

Let f be differentiable on the open interval (a,b) and continuous on the closed interval [a,b]. Then if f(a)=f(b), then there is at least one point c in (a,b) where f^'(c)=0. ...

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 function intx gives the integer part of x. In many computer languages, the function is denoted int(x). It is related to the floor and ceiling functions |_x_| and [x] by ...

The polar sine is a function of a vertex angle of an n-dimensional parallelotope or simplex. If the content of the parallelotope is P and the lengths of the n edges of the ...

Bertelsen's number is an erroneous name erroneously given to the erroneous value of pi(10^9)=50847478, where pi(x) is the prime counting function. This value is 56 lower than ...

A series is said to be convergent if it approaches some limit (D'Angelo and West 2000, p. 259). Formally, the infinite series sum_(n=1)^(infty)a_n is convergent if the ...

Given any straight line and a point not on it, there "exists one and only one straight line which passes" through that point and never intersects the first line, no matter ...

An angle bracket is the combination of a bra and ket (bra+ket = bracket) which represents the inner product of two functions or vectors (or 1-forms), <f|g>=intf(x)g^|(x)dx in ...