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A symmetric matrix is a square matrix that satisfies A^(T)=A, (1) where A^(T) denotes the transpose, so a_(ij)=a_(ji). This also implies A^(-1)A^(T)=I, (2) where I is the ...

For every even dimension 2n, the symplectic group Sp(2n) is the group of 2n×2n matrices which preserve a nondegenerate antisymmetric bilinear form omega, i.e., a symplectic ...

A transition function describes the difference in the way an object is described in two separate, overlapping coordinate charts, where the description of the same set may ...

A Vandermonde matrix is a type of matrix that arises in the polynomial least squares fitting, Lagrange interpolating polynomials (Hoffman and Kunze p. 114), and the ...

If X and Y are independent variates and X+Y is a normal distribution, then both X and Y must have normal distributions. This was proved by Cramér in 1936.

The Grassmannian Gr(n,k) is the set of k-dimensional subspaces in an n-dimensional vector space. For example, the set of lines Gr(n+1,1) is projective space. The real ...

An element of order 2 in a group (i.e., an element A of a group such that A^2=I, where I is the identity element).

An operator of period 2, i.e., an operator * which satisfies ((a)^*)^*=a.

A type of statistic which can be useful for determining asymmetry and tailedness of a population.

The orthogonal decomposition of a matrix into lower trapezoidal matrices.