Subspace

/ˈsʌb.speɪs/

Meaning & Definition

noun

A vector space that is a subset of another vector space, which is itself a vector space under the operations of vector addition and scalar multiplication.

In linear algebra, a plane in three-dimensional space can be considered a subspace of that space.

In topology, a subspace is a subset of a topological space that inherits the topology from the larger space.

The set of all open intervals in the real numbers forms a subspace of the larger space of real numbers.

In computer science, a subspace may refer to a reduced dimensionality representation of data.

The algorithm reduced the dataset to a subspace that captures the most variance.

Etymology

The word subspace is formed from the prefix 'sub-' meaning 'under' or 'below', and 'space'.

Common Phrases and Expressions

subspace communication

The exchange of information within a certain defined space in theoretical models.

subspace travel

A fictional method of traveling faster than light, often found in science fiction.

Related Words

vector space

A mathematical structure formed by a collection of vectors.

dimensionality

The number of dimensions in a space, important in defining subspaces.

Slang Meanings

A state of mind or altered perception, often used in a fictional or gaming context.

When I get into that meditative state, it feels like I'm in a subspace.

An environment or setting where the usual rules don't apply, often used in gaming.

The game's subspace allows us to escape enemy fire and regroup.