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The eigenvector corresponding to the second smallest eigenvalue (i.e., the algebraic connectivity) of the Laplacian matrix of a graph G. The Fiedler vector is used in ...

A linear functional defined on a subspace of a vector space V and which is dominated by a sublinear function defined on V has a linear extension which is also dominated by ...

A polynomial function of the elements of a vector x can be uniquely decomposed into a sum of harmonic polynomials times powers of |x|.

Let V!=(0) be a finite dimensional vector space over the complex numbers, and let A be a linear operator on V. Then V can be expressed as a direct sum of cyclic subspaces.

The upside-down capital delta symbol del , also called "del," used to denote the gradient and other vector derivatives. The following table summarizes the names and notations ...

A ruled surface M is a normal developable of a curve y if M can be parameterized by x(u,v)=y(u)+vN^^(u), where N is the normal vector (Gray 1993, pp. 352-354; first edition ...

Let A:D(A)->H and B:D(B)->H be linear operators from domains D(A) and D(B), respectively, into a Hilbert space H. It is said that B extends A if D(A) subset D(B) and if Bv=Av ...

The permutohedron is the n-dimensional generalization of the hexagon. The n-permutohedron is the convex hull of all permutations of the vector (x_1,x_2,...,x_(n+1)) in ...

Every Lie algebra L is isomorphic to a subalgebra of some Lie algebra A^-, where the associative algebra A may be taken to be the linear operators over a vector space V.

The index of a vector field with finitely many zeros on a compact, oriented manifold is the same as the Euler characteristic of the manifold.