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A quadratic form involving n real variables x_1, x_2, ..., x_n associated with the n×n matrix A=a_(ij) is given by Q(x_1,x_2,...,x_n)=a_(ij)x_ix_j, (1) where Einstein ...

The concept of a space is an extremely general and important mathematical construct. Members of the space obey certain addition properties. Spaces which have been ...

A distribution which arises in the study of half-integer spin particles in physics, P(k)=(k^s)/(e^(k-mu)+1). (1) Its integral is given by int_0^infty(k^sdk)/(e^(k-mu)+1) = ...

Given a matrix A, let |A| denote its determinant. Then |A||A_(rs,pq)|=|A_(r,p)||A_(s,q)|-|A_(r,q)||A_(s,p)|, (1) where A_(u,w) is the submatrix of A formed by the ...

The Lerch transcendent is generalization of the Hurwitz zeta function and polylogarithm function. Many sums of reciprocal powers can be expressed in terms of it. It is ...

The Spencer-Brown form is a simple mathematical concept that formalizes what a mathematical object is formally identical to what it is not (Spencer-Brown 1997, pp. ix and ...

Also known as "Laplacian" determinant expansion by minors, expansion by minors is a technique for computing the determinant of a given square matrix M. Although efficient for ...

A method for finding a matrix inverse. To apply Gauss-Jordan elimination, operate on a matrix [A I]=[a_(11) ... a_(1n) 1 0 ... 0; a_(21) ... a_(2n) 0 1 ... 0; | ... | | | ... ...

The polylogarithm Li_n(z), also known as the Jonquière's function, is the function Li_n(z)=sum_(k=1)^infty(z^k)/(k^n) (1) defined in the complex plane over the open unit ...

Gaussian elimination is a method for solving matrix equations of the form Ax=b. (1) To perform Gaussian elimination starting with the system of equations [a_(11) a_(12) ... ...