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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. ...

A topological algebra is a pair (A,tau), where A=(A,(f_i^A)_(i in I)) is an algebra and each of the operations f_i^A is continuous in the product topology. Examples of ...

The vector triple product identity is also known as the BAC-CAB identity, and can be written in the form Ax(BxC) = B(A·C)-C(A·B) (1) (AxB)xC = -Cx(AxB) (2) = -A(B·C)+B(A·C). ...

Affine functions represent vector-valued functions of the form f(x_1,...,x_n)=A_1x_1+...+A_nx_n+b. The coefficients can be scalars or dense or sparse matrices. The constant ...

A Hilbert space is a vector space H with an inner product <f,g> such that the norm defined by |f|=sqrt(<f,f>) turns H into a complete metric space. If the metric defined by ...

The tensor product between modules A and B is a more general notion than the vector space tensor product. In this case, we replace "scalars" by a ring R. The familiar ...

The Siegel theta function is a Gamma_n-invariant meromorphic function on the space of all p×p symmetric complex matrices Z=X+iY with positive definite imaginary part. It is ...

A vector space with a T2-space topology such that the operations of vector addition and scalar multiplication are continuous. The interesting examples are ...

The torsion of a space curve, sometimes also called the "second curvature" (Kreyszig 1991, p. 47), is the rate of change of the curve's osculating plane. The torsion tau is ...

A vector Laplacian can be defined for a vector A by del ^2A=del (del ·A)-del x(del xA), (1) where the notation ✡ is sometimes used to distinguish the vector Laplacian from ...