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A k-matrix is a kind of cube root of the identity matrix (distinct from the identity matrix) which is defined by the complex matrix k=[0 0 -i; i 0 0; 0 1 0]. It satisfies ...

The absolute value of a real number x is denoted |x| and defined as the "unsigned" portion of x, |x| = xsgn(x) (1) = {-x for x<=0; x for x>=0, (2) where sgn(x) is the sign ...

There are at least two statements which go by the name of Artin's conjecture. If r is any complex finite-dimensional representation of the absolute Galois group of a number ...

Let the characteristic polynomial of an n×n complex matrix A be written in the form P(lambda) = |lambdaI-A| (1) = ...

A bilinear form on a real vector space is a function b:V×V->R that satisfies the following axioms for any scalar alpha and any choice of vectors v,w,v_1,v_2,w_1, and w_2. 1. ...

A branch cut is a curve (with ends possibly open, closed, or half-open) in the complex plane across which an analytic multivalued function is discontinuous. For convenience, ...

The canonical bundle is a holomorphic line bundle on a complex manifold which is determined by its complex structure. On a coordinate chart (z_1,...z_n), it is spanned by the ...

Each Cartan matrix determines a unique semisimple complex Lie algebra via the Chevalley-Serre, sometimes called simply the "Serre relations." That is, if (A_(ij)) is a k×k ...

The complementary subspace problem asks, in general, which closed subspaces of a Banach space are complemented (Johnson and Lindenstrauss 2001). Phillips (1940) proved that ...

The complex structure of a point x=x_1,x_2 in the plane is defined by the linear map J:R^2->R^2 J(x_1,x_2)=(-x_2,x_1), (1) and corresponds to a counterclockwise rotation by ...