For every vector space there exists a basis,^{} and all bases of a vector space have equal cardinality;^{} as a result, the dimension of a vector space is uniquely defined. We say *V* is **finite-dimensional** if the dimension of *V* is finite, and **infinite-dimensional** if its dimension is infinite.

The dimension of the vector space *V* over the field *F* can be written as dim_{F}(*V*) or as , read "dimension of *V* over *F*". When *F* can be inferred from context, dim(*V*) is typically written.

The vector space **R**^{3} has

as a basis, and therefore we have dim_{R}(**R**^{3}) = 3. More generally, dim_{R}(**R**^{n}) = *n*, and even more generally, dim_{F}(*F*^{n}) = *n* for any field *F*.

The complex numbers **C** are both a real and complex vector space; we have dim_{R}(**C**) = 2 and dim_{C}(**C**) = 1. So the dimension depends on the base field.

This page was last edited on 16 May 2018, at 15:26.

Reference: https://en.wikipedia.org/wiki/Dimension_of_a_vector_space under CC BY-SA license.

Reference: https://en.wikipedia.org/wiki/Dimension_of_a_vector_space under CC BY-SA license.

- Mathematics
- Vector Space
- Cardinality
- Basis
- Field
- Georg Hamel
- Dimension
- Finite
- Infinite
- Basis
- Field
- Complex Numbers

- Dimension Of A Vector Space
- La Salle Greenhills
- Wrenboys
- The Case Of The Dean Of St Asaph
- Bridge Of Four Lions
- Snake River Stampede Rodeo
- C%C3%A9sar Delgado
- El Chavo: The Animated Series
- Bounce (Iggy Azalea Song)
- Sam Samudio
- The Spirit Of Laws
- Shush, Iran
- Peace Rally
- Kittanning Expedition
- East Nashville
- Matthew Sutcliffe
- Andreas Rass
- Luckyhorse Industries
- Kruskal Tree Theorem
- Cecil B. Moore, Philadelphia
- Template:Infobox Country
- Next Generation Adelaide International
- Pushlets
- Danny Pudi
- United Arab Emirates Women%27s National Cricket Team
- Sparks Fly (album)
- Launceston Church Of England Grammar School
- BoxTV.com
- Emergency Action Message
- Pilar, Argentina