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A typical vector (i.e., a vector such as the radius vector r) is transformed to its negative under inversion of its coordinate axes. Such "proper" vectors are known as polar ...

The modulus of a complex number z, also called the complex norm, is denoted |z| and defined by |x+iy|=sqrt(x^2+y^2). (1) If z is expressed as a complex exponential (i.e., a ...

Let B_n(r) be the n-dimensional closed ball of radius r>1 centered at the origin. A function which is defined on B(r) is called an extension to B(r) of a function f defined ...

A real-linear vector space H equipped with a symplectic form s.

The word basis can arise in several different contexts. Speaking in general terms, an object is "generated" by a basis in whatever manner is appropriate. For example, a ...

The "perp dot product" a^_|_·b for a and b vectors in the plane is a modification of the two-dimensional dot product in which a is replaced by the perpendicular vector ...

An action with G=R. Flows are generated by vector fields and vice versa.

The kernel of a linear transformation T:V-->W between vector spaces is its null space.

A special case of a flag manifold. A Grassmann manifold is a certain collection of vector subspaces of a vector space. In particular, g_(n,k) is the Grassmann manifold of ...

A Banach space X is called minimal if every infinite-dimensional subspace Y of X contains a subspace Z isomorphic to X. An example of a minimal Banach space is the Banach ...