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Let K be a finite complex, and let phi:C_p(K)->C_p(K) be a chain map, then sum_(p)(-1)^pTr(phi,C_p(K))=sum_(p)(-1)^pTr(phi_*,H_p(K)/T_p(K)).

Let V!=(0) be a finite dimensional vector space over the complex numbers, and let A be a linear operator on V. Then V can be expressed as a direct sum of cyclic subspaces.

If K is a finite complex and h:|K|->|K| is a continuous map, then Lambda(h)=sum(-1)^pTr(h_*,H_p(K)/T_p(K)) is the Lefschetz number of the map h.

A line bundle is a special case of a vector bundle in which the fiber is either R, in the case of a real line bundle, or C, in the case of a complex line bundle.

A matrix A for which A^(H)=A^(T)^_=A, where the conjugate transpose is denoted A^(H), A^(T) is the transpose, and z^_ is the complex conjugate. If a matrix is self-adjoint, ...

The single bar | is a notation variously used to denote the absolute value |x|, complex modulus |z|, vector norm |x|, determinant |A|, or "divides" (a|b).

The image on the Riemann sphere of any circle under a complex rational mapping with numerator and denominator having degrees no more than n has length no longer than 2npi.

An element of an extension field of a field F which is not algebraic over F. A transcendental number is a complex number which is transcendental over the field Q of rational ...

The space |K| which is the subset of R^n that is the union of the simplices in a simplicial complex K. The term polytope is sometimes used as a synonym for underlying space ...

There are at least two meanings of the term "total derivative" in mathematics. The first is as an alternate term for the convective derivative. The total derivative is the ...