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Let V be an n-dimensional linear space over a field K, and let Q be a quadratic form on V. A Clifford algebra is then defined over T(V)/I(Q), where T(V) is the tensor algebra ...

There are two sorts of transforms known as the fractional Fourier transform. The linear fractional Fourier transform is a discrete Fourier transform in which the exponent is ...

The circle H which touches the incircles I, I_A, I_B, and I_C of a circular triangle ABC and its associated triangles. It is either externally tangent to I and internally ...

The multicomputational paradigm is a generalization of the computational paradigm to many computational threads of time. In the ordinary computational paradigm, time ...

An equation of the form f(x)=b (mod m), (1) where the values of 0<=x<m for which the equation holds are sought. Such an equation may have none, one, or many solutions. There ...

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 ...

The Killing form is an inner product on a finite dimensional Lie algebra g defined by B(X,Y)=Tr(ad(X)ad(Y)) (1) in the adjoint representation, where ad(X) is the adjoint ...

Let A be an involutive algebra over the field C of complex numbers with involution xi|->xi^♭. Then A is a right Hilbert algebra if A has an inner product <·,·> satisfying: 1. ...

The inverse of a square matrix A, sometimes called a reciprocal matrix, is a matrix A^(-1) such that AA^(-1)=I, (1) where I is the identity matrix. Courant and Hilbert (1989, ...

The simplex method is a method for solving problems in linear programming. This method, invented by George Dantzig in 1947, tests adjacent vertices of the feasible set (which ...