Live briefing
Everything about Linear map
Mathematical function, in linear algebra
In mathematics, and more specifically in linear algebra, a linear map, linear mapping, or linear operator is a particular kind of function between vector spaces, which respects the basic operations of vector addition and scalar multiplication. A standard example of a linear map is an matrix, which takes vectors in -dimensions into vectors in -dimensions in a way that is compatible with addition of vectors, and multiplication of vectors by scalars. When the two vector spaces are the same, a linear map is also called a linear transformation or linear endomorphism. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Linear mapA 5-minute orientation
- Skim a recent paper: Hardware architecture of a digital piecewise linear chaotic map with perturbation for pseudorandom number generationInfluential work since 2022
- Pick up a classic book: Stabilisation de la formule des traces tordueThe most-reprinted book on the subject
- Read the landmark paper: Statistical parametric maps in functional imaging: A general linear approachCited 7,944 times
- Go sideways: Linear formA closely related topic
- Go sideways: Vector spaceA closely related topic
📖 Definitions
Noun Synonym of linear transformation.
🏆 Landmark papers (most cited)
Statistical parametric maps in functional imaging: A general linear approach
Inhomogeneity correction using an estimated linear field map
Physical map of the linear chromosome of Streptomyces griseus
Dynamics of a piecewise linear map with a gap
Invariant circles for the piecewise linear standard map
Deterministic stochastic resonance in a piecewise linear chaotic map
Piecewise Linear Rubber-Sheet Map Transformation
Air Traffic Complexity Map Based on Linear Dynamical Systems
🆕 Influential since 2022
Hardware architecture of a digital piecewise linear chaotic map with perturbation for pseudorandom number generation
Border-collision bifurcation route to strange nonchaotic attractors in the piecewise linear normal form map
Perception of Fundamental Values and Financial Market Dynamics: Mathematical Insights from a 2D Piecewise Linear Map
Multiple image encryption approach using non linear chaotic map and cosine transformation
Sparse connectivity for MAP inference in linear models using sister mitral cells
📚 Books worth reading
Stabilisation de la formule des traces tordueColette Moeglin, Jean-Loup Waldspurger · 2016
Advanced engineering mathematicsGreenberg, Michael D. · 1988
Similarity problems and completely bounded mapsGilles Pisier · 1996
Optimization with multivalued mappingsStephan Dempe · 2006
Combinatorial dynamics and entropy in dimension oneLl Alsedà, Lluis Alseda · 1993- 📕On right translation in Teichmuller's spaceFrederick P. Gardiner · 1967
Differential calculus in topological linear spacesSadayuki Yamamuro · 1974- 📕An inverse problem in thermal imagingKurt Bryan · 1994
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- 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…
- Vector space In mathematics, a vector space (also called a linear space) is a set whose elements, often called vectors, can be added together and multiplied ("scaled")…
- 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…
- Projection (linear algebra) In linear algebra and functional analysis, a projection is a linear transformation P from a vector space to itself (an endomorphism) such that P∘P=P. That…
- 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…
- Trace (linear algebra) In linear algebra, the trace of a square matrix A, denoted tr(A), is defined as a sum of the elements on its main diagonal, a11+a22+⋯+ann. It is only defined…
- Dual norm In functional analysis, the dual norm is a measure of size for a continuous linear function defined on a normed vector space. Let X be a normed vector…
- Jordan normal form [⌜λ11⌝λ11⌞λ1⌟⌜λ21⌝⌞λ2⌟[λ3]⋱⌜λn1⌝⌞λn⌟] Example of a matrix in Jordan normal form. All matrix entries not shown are zero. The outlined squares are known…