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An (m+1)-dimensional subspace W of an (n+1)-dimensional vector space V can be specified by an (m+1)×(n+1) matrix whose rows are the coordinates of a basis of W. The set of ...

A univariate distribution proportional to the F-distribution. If the vector d is Gaussian multivariate-distributed with zero mean and unit covariance matrix N_p(0,I) and M is ...

Admitting an inverse. An object that is invertible is referred to as an invertible element in a monoid or a unit ring, or to a map, which admits an inverse map iff it is ...

Given a map f:S->T between sets S and T, the map g:T->S is called a left inverse to f provided that g degreesf=id_S, that is, composing f with g from the left gives the ...

If g is a Lie algebra, then a subspace a of g is said to be a Lie subalgebra if it is closed under the Lie bracket. That is, a is a Lie subalgebra of g if for all x,y in a, ...

Given a map f from a space X to a space Y and another map g from a space Z to a space Y, a lift is a map h from X to Z such that gh=f. In other words, a lift of f is a map h ...

Let X be a locally convex topological vector space and let K be a compact subset of X. In functional analysis, Milman's theorem is a result which says that if the closed ...

The orthogonal complement of a subspace V of the vector space R^n is the set of vectors which are orthogonal to all elements of V. For example, the orthogonal complement of ...

Given a map f:S->T between sets S and T, the map g:T->S is called a right inverse to f provided that f degreesg=id_T, that is, composing f with g from the right gives the ...

A Lie algebra g is solvable when its Lie algebra commutator series, or derived series, g^k vanishes for some k. Any nilpotent Lie algebra is solvable. The basic example is ...