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The total number of contravariant and covariant indices of a tensor. The rank R of a tensor is independent of the number of dimensions N of the underlying space. An intuitive ...

Tomography is the study of the reconstruction of two- and three-dimensional objects from one-dimensional slices. The Radon transform is an important tool in tomography. ...

Let H be a Hilbert space and (e_i)_(i in I) an orthonormal basis for H. The set of all products of two Hilbert-Schmidt operators is denoted N(H), and its elements are called ...

The trapezo-rhombic dodecahedron, also called the rhombo-trapezoidal dodecahedron, is a general dodecahedron consisting of six identical rhombi and six identical isosceles ...

Triangle picking is the process of picking triangles at random within a given shape in the plane, in space, or in a higher dimension. The most natural definition of a random ...

A vector basis of a vector space V is defined as a subset v_1,...,v_n of vectors in V that are linearly independent and span V. Consequently, if (v_1,v_2,...,v_n) is a list ...

If W is a k-dimensional subspace of a vector space V with inner product <,>, then it is possible to project vectors from V to W. The most familiar projection is when W is the ...

A smooth two-dimensional surface given by embedding the projective plane into projective 5-space by the homogeneous parametric equations v(x,y,z)=(x^2,y^2,z^2,xy,xz,yz). The ...

Wavelets are a class of a functions used to localize a given function in both space and scaling. A family of wavelets can be constructed from a function psi(x), sometimes ...

Let X=(X,tau) be a topological vector space whose continuous dual X^* may or may not separate points (i.e., may or may not be T2). The weak-* (pronounced "weak star") ...