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The Kronecker sum is the matrix sum defined by A direct sum B=A tensor I_b+I_a tensor B, (1) where A and B are square matrices of order a and b, respectively, I_n is the ...

The normal vector, often simply called the "normal," to a surface is a vector which is perpendicular to the surface at a given point. When normals are considered on closed ...

The Dirac matrices are a class of 4×4 matrices which arise in quantum electrodynamics. There are a variety of different symbols used, and Dirac matrices are also known as ...

If A is a graded module and there exists a degree-preserving linear map phi:A tensor A->A, then (A,phi) is called a graded algebra. Cohomology is a graded algebra. In ...

Orthogonal contravariant and covariant satisfy g_(ik)g^(ij)=delta_k^j, where delta_j^k is the Kronecker delta.

A knot invariant is a function from the set of all knots to any other set such that the function does not change as the knot is changed (up to isotopy). In other words, a ...

A Hermitian metric on a complex vector bundle assigns a Hermitian inner product to every fiber bundle. The basic example is the trivial bundle pi:U×C^k->U, where U is an open ...

The power series that defines the exponential map e^x also defines a map between matrices. In particular, exp(A) = e^(A) (1) = sum_(n=0)^(infty)(A^n)/(n!) (2) = ...

Let A be a commutative ring and let C_r be an R-module for r=0,1,2,.... A chain complex C__ of the form C__:...|->C_n|->C_(n-1)|->C_(n-2)|->...|->C_2|->C_1|->C_0 is said to ...

Arc length is defined as the length along a curve, s=int_gamma|dl|, (1) where dl is a differential displacement vector along a curve gamma. For example, for a circle of ...