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Eigenvalues are a special set of scalars associated with a linear system of equations (i.e., a matrix equation) that are sometimes also known as characteristic roots, ...

A root of a polynomial P(z) is a number z_i such that P(z_i)=0. The fundamental theorem of algebra states that a polynomial P(z) of degree n has n roots, some of which may be ...

The identity sum_(y=0)^m(m; y)(w+m-y)^(m-y-1)(z+y)^y=w^(-1)(z+w+m)^m (Bhatnagar 1995, p. 51). There are a host of other such binomial identities.

The word adjoint has a number of related meanings. In linear algebra, it refers to the conjugate transpose and is most commonly denoted A^(H). The analogous concept applied ...

Let K be a field, and A a K-algebra. Elements y_1, ..., y_n are algebraically independent over K if the natural surjection K[Y_1,...,Y_n]->K[y_1,...,y_n] is an isomorphism. ...

The arithmetic-geometric index of a graph is defined as half the sum of the matrix elements of its arithmetic-geometric matrix.

Bailey's transformation is the very general hypergeometric transformation (1) where k=1+2a-b-c-d, and the parameters are subject to the restriction b+c+d+e+f+g-m=2+3a (2) ...

The Wolfram Physics Project posits the existence of abstract relations between atoms of space whose pattern defines the structure of physical space. In this approach, two ...

The term "Cartesian" is used to refer to anything that derives from René Descartes' conception of geometry (1637), which is based on the representation of points in the plane ...

The downward Clenshaw recurrence formula evaluates a sum of products of indexed coefficients by functions which obey a recurrence relation. If f(x)=sum_(k=0)^Nc_kF_k(x) (1) ...