Matrix Groups

URI: https://gptkb.org/entity/Matrix_Groups
GPTKB entity
Properties (50)
Predicate Object
gptkbp:instanceOf musical group
gptkbp:hasExhibition General_Linear_Group_(GL(n))
Matrix_Lie_Groups
Orthogonal_Group_(O(n))
Projective_General_Linear_Group_(PGL(n))
Special_Linear_Group_(SL(n))
Symplectic_Group_(Sp(n))
Unitary_Group_(U(n))
gptkbp:hasSpecialty Closed under matrix multiplication
Associative operation
Contains identity matrix
Contains inverses for every element
https://www.w3.org/2000/01/rdf-schema#label Matrix Groups
gptkbp:isCharacterizedBy Dimension in terms of matrix size
Group operation defined by matrix multiplication
Matrix representation of group elements
Set of invertible matrices
Topology induced by matrix norm
gptkbp:isRelatedTo gptkb:Algebraic_Groups
gptkb:Topological_Groups
Cohomology
Eigenvalues
Topology
Matrix Factorization
Abstract Algebra
Rank
Functional Analysis
Determinants
Differential Geometry
Eigenvectors
Representation Theory
Group Theory
Lie Algebras
Group Actions
Homology
Subgroups
Normal Subgroups
Finite Groups
Homomorphisms
Isomorphisms
Trace
Simple Groups
Automorphisms
Singular_Value_Decomposition_(SVD)
Symmetry_Groups
gptkbp:isUsedIn gptkb:Quantum_Mechanics
Robotics
Control Theory
Computer_Graphics
Linear_Algebra