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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; ...

Vector subtraction is the process of taking a vector difference, and is the inverse operation to vector addition.

There are many formulas of pi of many types. Among others, these include series, products, geometric constructions, limits, special values, and pi iterations. pi is ...