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The difference between a quantity and its estimated or measured quantity.

A connection between two or more vertices of a hypergraph. A hyperedge connecting just two vertices is simply a usual graph edge.

Two quantities y and x are said to be inversely proportional (or "in inverse proportion") if y is given by a constant multiple of 1/x, i.e., y=c/x for c a constant. This ...

A square matrix which is not reducible is said to be irreducible.

Topological lower bounds in terms of Betti numbers for the number of critical points form a smooth function on a smooth manifold.

A group whose group operation is identified with multiplication. As with normal multiplication, the multiplication operation on group elements is either denoted by a raised ...

A vector space possessing a norm.

A mathematical structure (e.g., a group, vector space, or smooth manifold) in a category.

Euclidean n-space is denoted R^n.

A square matrix U is a unitary matrix if U^(H)=U^(-1), (1) where U^(H) denotes the conjugate transpose and U^(-1) is the matrix inverse. For example, A=[2^(-1/2) 2^(-1/2) 0; ...