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For any nonzero lambda in C, either 1. The equation Tv-lambdav=0 has a nonzero solution v, or 2. The equation Tv-lambdav=f has a unique solution v for any function f. In the ...

The eigenvalues of a graph are defined as the eigenvalues of its adjacency matrix. The set of eigenvalues of a graph is called a graph spectrum. The largest eigenvalue ...

A property that passes from a topological space to every subspace with respect to the relative topology. Examples are first and second countability, metrizability, the ...

A Hermitian form on a vector space V over the complex field C is a function f:V×V->C such that for all u,v,w in V and all a,b in R, 1. f(au+bv,w)=af(u,w)+bf(v,w). 2. ...

A Hermitian inner product on a complex vector space V is a complex-valued bilinear form on V which is antilinear in the second slot, and is positive definite. That is, it ...

A minimal embedded surface discovered in 1992 consisting of a helicoid with a hole and handle (Science News 1992). It has the same topology as a punctured sphere with a ...

A continuous transformation from one function to another. A homotopy between two functions f and g from a space X to a space Y is a continuous map G from X×[0,1]|->Y such ...

A hypothesis is a proposition that is consistent with known data, but has been neither verified nor shown to be false. In statistics, a hypothesis (sometimes called a ...

A differential ideal is an ideal I in the ring of smooth forms on a manifold M. That is, it is closed under addition, scalar multiplication, and wedge product with an ...

There are several results known as the Morgado identity. The first is (1) where F_n is a Fibonacci number and L_n is a Lucas number (Morgado 1987, Dujella 1995). A second ...