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A covariant tensor, denoted with a lowered index (e.g., a_mu) is a tensor having specific transformation properties. In general, these transformation properties differ from ...

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 ...

Using a Tschirnhausen transformation, the principal quintic form can be transformed to the one-parameter form w^5-10cw^3+45c^2w-c^2=0 (1) named after Francesco Brioschi ...

An infinitesimal transformation of a vector r is given by r^'=(I+e)r, (1) where the matrix e is infinitesimal and I is the identity matrix. (Note that the infinitesimal ...

A bijective map between two metric spaces that preserves distances, i.e., d(f(x),f(y))=d(x,y), where f is the map and d(a,b) is the distance function. Isometries are ...

A matrix used in the Jacobi transformation method of diagonalizing matrices. The Jacobi rotation matrix P_(pq) contains 1s along the diagonal, except for the two elements ...

1. Find a complete system of invariants, or 2. Decide when two metrics differ only by a coordinate transformation. The most common statement of the problem is, "Given metrics ...

Because even high-resolution computer monitors have a relatively small number of pixels, when graphics or text display distinguish between individual pixels. The result is ...

A binary plot of an integer sequence is a plot of the binary representations of successive terms where each term is represented as a column of bits with 1s colored black and ...

A function H that maps an arbitrary length message M to a fixed length message digest MD is a collision-free hash function if 1. It is a one-way hash function. 2. It is hard ...