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Bertrand's postulate, also called the Bertrand-Chebyshev theorem or Chebyshev's theorem, states that if n>3, there is always at least one prime p between n and 2n-2. ...

The differential forms on C^n decompose into forms of type (p,q), sometimes called (p,q)-forms. For example, on C, the exterior algebra decomposes into four types: ^ C = ^ ^0 ...

A matrix, also called a canonical box matrix, having zeros everywhere except along the diagonal and superdiagonal, with each element of the diagonal consisting of a single ...

The Jordan canonical form, also called the classical canonical form, of a special type of block matrix in which each block consists of Jordan blocks with possibly differing ...

In n-dimensional Lorentzian space R^n=R^(1,n-1), the light cone C^(n-1) is defined to be the subset consisting of all vectors x=(x_0,x_1,...,x_(n-1)) (1) whose squared ...

Nonhomogeneous matrix equations of the form Ax=b (1) can be solved by taking the matrix inverse to obtain x=A^(-1)b. (2) This equation will have a nontrivial solution iff the ...

The Radon-Nikodym theorem asserts that any absolutely continuous complex measure lambda with respect to some positive measure mu (which could be Lebesgue measure or Haar ...

Let A be an n×n matrix over a field F. Using the three elementary row and column operations over elements in the field, the n×n matrix xI-A with entries from the principal ...

In an integral domain R, the decomposition of a nonzero noninvertible element a as a product of prime (or irreducible) factors a=p_1...p_n, (1) is unique if every other ...

A representation of a group G is a group action of G on a vector space V by invertible linear maps. For example, the group of two elements Z_2={0,1} has a representation phi ...