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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 ...

Given a real m×n matrix A, there are four associated vector subspaces which are known colloquially as its fundamental subspaces, namely the column spaces and the null spaces ...

An integral of the form intf(z)dz, (1) i.e., without upper and lower limits, also called an antiderivative. The first fundamental theorem of calculus allows definite ...

The set of all nonsingular affine transformations of a translation in space constitutes a group known as the affine group. The affine group contains the full linear group and ...

A Banach limit is a bounded linear functional f on the space ł^infty of complex bounded sequences that satisfies ||f||=f(1)=1 and f({a_(n+1)})=f({a_n}) for all {a_n} in ...

A technically defined group characterizing a system of linear differential equations y_j^'=sum_(k=1)^na_(jk)(x)y_k for j=1, ..., n, where a_(jk) are complex analytic ...

A perfect cubic polynomial can be factored into a linear and a quadratic term, x^3+y^3 = (x+y)(x^2-xy+y^2) (1) x^3-y^3 = (x-y)(x^2+xy+y^2). (2)

Let A and B be C^*-algebras, then a linear map phi:A->B is said to be positive if phi(A_+) subset= B_+. Here, A_+ is denoted the positive part of A. For example, every ...

If pi on V and pi^' on V^' are irreducible representations and E:V|->V^' is a linear map such that pi^'(g)E=Epi(g) for all g in and group G, then E=0 or E is invertible. ...

Given a subalgebra A of the algebra B(H) of bounded linear transformations from a Hilbert space H onto itself, the vector v in H is a separating vector for A if the only ...