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Cospectral graphs, also called isospectral graphs, are graphs that share the same graph spectrum. The smallest pair of isospectral graphs is the graph union C_4 union K_1 and ...

Exterior algebra is the algebra of the wedge product, also called an alternating algebra or Grassmann algebra. The study of exterior algebra is also called Ausdehnungslehre ...

A fiber bundle (also called simply a bundle) with fiber F is a map f:E->B where E is called the total space of the fiber bundle and B the base space of the fiber bundle. The ...

In the Minkowski space of special relativity, a four-vector is a four-element vector x^mu=(x^0,x^1,x^2,x^3) that transforms under a Lorentz transformation like the position ...

The standard Lorentzian inner product on R^4 is given by -dx_0^2+dx_1^2+dx_2^2+dx_3^2, (1) i.e., for vectors v=(v_0,v_1,v_2,v_3) and w=(w_0,w_1,w_2,w_3), ...

Lorentzian n-space is the inner product space consisting of the vector space R^n together with the n-dimensional Lorentzian inner product. In the event that the (1,n-1) ...

The word polytope is used to mean a number of related, but slightly different mathematical objects. A convex polytope may be defined as the convex hull of a finite set of ...

Topology

An nth-rank tensor in m-dimensional space is a mathematical object that has n indices and m^n components and obeys certain transformation rules. Each index of a tensor ranges ...

An inner product is a generalization of the dot product. In a vector space, it is a way to multiply vectors together, with the result of this multiplication being a scalar. ...