normed vector space

This is the standard topology on any normed vector space.

It is not specifically the inner product on a normed vector space.

Together with these maps, normed vector spaces form a category.

In the case of a normed vector space, the statement is:

The open and closed balls in a normed vector space are balanced sets.

In a semi normed vector space the closed unit ball is a barrel.

Measures of non-compactness are most commonly used if M is a normed vector space.

For this reason, not every scalar product space is a normed vector space.

Normed vector spaces are central to the study of linear algebra and functional analysis.

He was one of the first mathematicians to apply normed vector spaces in numerical analysis.

The idea of normed vector space was in the air, and in the 1920s Banach created functional analysis.

In a normed vector space there is only one vector of norm equal to 0.

Normed vector spaces also define an operation known as the norm (or determination of magnitude).

A vector space with a norm is called a normed vector space.

Isometrically isomorphic normed vector spaces are identical for all practical purposes.

The most important maps between two normed vector spaces are the continuous linear maps.

Normed vector space: a vector space with a compatible norm.

Formally, it is a norm defined on the space of bounded linear operators between two given normed vector spaces.

In other words, in the category of normed vector spaces, the space K is an injective object.

The closed unit ball of the dual of a normed vector space over the reals has an extreme point.

The basic and historically first class of spaces studied in functional analysis are complete normed vector spaces over the real or complex numbers.

Hamilton's tensor is actually the absolute value on the quaternion algebra, which makes it a normed vector space.

In the case of normed vector spaces, the last property can be made stronger using the Krull sharpening to:

Let be a real normed vector space, and let be the dual space to .

When speaking of normed vector spaces, we augment the notion of dual space to take the norm into account.