Everything about Vector space
Algebraic structure in linear algebra
In mathematics, a vector space is a set whose elements, often called vectors, can be added together and multiplied ("scaled") by numbers called scalars. The operations of vector addition and scalar multiplication must satisfy certain requirements, called vector axioms. Real vector spaces and complex vector spaces are kinds of vector spaces based on different kinds of scalars: real numbers and complex numbers. Scalars can also be, more generally, elements of any field. Wikipedia →
🧠Start here: a 6-step reading path
- Read the overview: Vector spaceA 5-minute orientation
- Skim a recent paper: Vector space-time wave packetsInfluential work since 2022
- Pick up a classic book: A Course in Mathematical AnalysisThe most-reprinted book on the subject
- Read the landmark paper: A vector space model for automatic indexingCited 5,057 times
- Go sideways: Examples of vector spacesA closely related topic
- Go sideways: Linear mapA closely related topic
đź“– Definitions
Noun A set of elements called vectors, together with some field and operations called addition (mapping two vectors to a vector) and scalar multiplication (mapping a vector and an element in the field to a vector), satisfying a list of constraints; equivalently, a module over a field.
🏆 Landmark papers (most cited)
A vector space model for automatic indexing
Space vector PWM control of dual three-phase induction machine using vector space decomposition
A Space Vector PWM Scheme for Multilevel Inverters Based on Two-Level Space Vector PWM
Multilevel Multiphase Space Vector PWM Algorithm
Latent Space Cartography: Visual Analysis of Vector Space Embeddings
A New Space Vector Modulation Scheme for Multilevel Inverters Which Directly Vector Quantize the Reference Space Vector
Partitions of a vector space
Hidden Space Support Vector Machines
🆕 Influential since 2022
đź“š Books worth reading
A Course in Mathematical AnalysisD. J. H. Garling · 2013
Optimization by Vector Space MethodsDavid G. Luenberger, David G. Luenberger · 1968
Finite-dimensional vector spacesPaul R. Halmos · 1942- 📕Finite-dimensional vector spacesPaul R. Halmos · 1947
An introduction to frames and Riesz basesOle Christensen · 2002
Espaces topologiques, fonctions multivoquesClaude Berge · 1963
Linear topological spacesKelley, John L., J. L. Kelley · 1963
Abstract algebraDavid S. Dummit · 1991
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
đź”— Related topics
- Examples of vector spaces This page lists some examples of vector spaces. See vector space for the definitions of terms used on this page. See also: dimension, basis. Notation.…
- Linear map In mathematics, and more specifically in linear algebra, a linear map, linear mapping, or linear operator is a particular kind of function between vector…
- Linear algebra Linear algebra is the branch of mathematics concerning linear equations such as a1x1+⋯+anxn=b, linear maps such as the following: (x1,…,xn)↦a1x1+⋯+anxn…
- Functional (mathematics) In functional analysis, a functional is a map from a vector space to its underlying field. Elements of this field are called scalars, typically real or…
- Linear subspace In mathematics, and more specifically in linear algebra, a linear subspace or vector subspace is a vector space that is a subset of some larger vector…
- Kernel (linear algebra) In mathematics, the kernel of a linear map, also known as the null space or nullspace, is the part of the domain which is mapped to the zero vector of…
- Dual space In mathematics, every vector space V has a corresponding dual vector space (or just dual space for short) consisting of all linear forms on V, together…
- Linear form In mathematics, a linear form (also known as a linear functional, a one-form, or a covector) is a linear map from a vector space to its field of scalars…