http://dbpedia.org/ontology/abstract
|
En àlgebra lineal, una matriu defectiva és … En àlgebra lineal, una matriu defectiva és una matriu quadrada que no té una base completa de vectors propis, i és per això no diagonalizable. En particular, una matriu n × n és defectiva si i només si no té n vectors propis linealment independents. Es crea una base completa augmentant els vectors propis amb vectors propis generalitzats, que són necessaris per solucionar sistemes defectius d'equacions diferencials ordinàries i altres problemes. Una matriu n × n defectiva sempre té menys que n valors propis diferents, ja que quan els valors propis són diferents tenen vectors propis linealment independents. En particular, una matriu defectiva té un o més valors propis λ amb multiplicitat algebraica m > 1 (és a dir, les arrels del seu polinomi característic són múltiples), però menys d'm vectors propis linealment independents associats a λ. Si la multiplicitat algebraica de λ supera la seva multiplicitat geomètrica (és a dir, el número de vectors propis linealment independents associats a λ), llavors λ és anomenat valor propi defectiu. Tanmateix, cada valor propi amb multiplicitat algebraica m sempre té m vectors propis generalitzats independents. Una matriu hermítica (o el cas particular en els reals d'una matriu simètrica) o una matriu unitària mai és defectiva. Més generalment, una matriu normal (quin inclou l'hermítica i la unitària com a casos especials) mai és defectiva.a com a casos especials) mai és defectiva.
, In linear algebra, a defective matrix is a … In linear algebra, a defective matrix is a square matrix that does not have a complete basis of eigenvectors, and is therefore not diagonalizable. In particular, an n × n matrix is defective if and only if it does not have n linearly independent eigenvectors. A complete basis is formed by augmenting the eigenvectors with generalized eigenvectors, which are necessary for solving defective systems of ordinary differential equations and other problems. An n × n defective matrix always has fewer than n distinct eigenvalues, since distinct eigenvalues always have linearly independent eigenvectors. In particular, a defective matrix has one or more eigenvalues λ with algebraic multiplicity m > 1 (that is, they are multiple roots of the characteristic polynomial), but fewer than m linearly independent eigenvectors associated with λ. If the algebraic multiplicity of λ exceeds its geometric multiplicity (that is, the number of linearly independent eigenvectors associated with λ), then λ is said to be a defective eigenvalue. However, every eigenvalue with algebraic multiplicity m always has m linearly independent generalized eigenvectors. A Hermitian matrix (or the special case of a real symmetric matrix) or a unitary matrix is never defective; more generally, a normal matrix (which includes Hermitian and unitary as special cases) is never defective.tary as special cases) is never defective.
|
http://dbpedia.org/ontology/wikiPageExternalLink
|
https://archive.org/details/linearalgebraits00stra%7Curl-access=registration%7Cedition=3rd +
|
http://dbpedia.org/ontology/wikiPageID
|
5302952
|
http://dbpedia.org/ontology/wikiPageLength
|
4067
|
http://dbpedia.org/ontology/wikiPageRevisionID
|
1121771354
|
http://dbpedia.org/ontology/wikiPageWikiLink
|
http://dbpedia.org/resource/Ordinary_differential_equation +
, http://dbpedia.org/resource/Johns_Hopkins_University_Press +
, http://dbpedia.org/resource/Basis_%28linear_algebra%29 +
, http://dbpedia.org/resource/If_and_only_if +
, http://dbpedia.org/resource/Linear_algebra +
, http://dbpedia.org/resource/Generalized_eigenvector +
, http://dbpedia.org/resource/Eigenvector +
, http://dbpedia.org/resource/Linearly_independent +
, http://dbpedia.org/resource/Hermitian_matrix +
, http://dbpedia.org/resource/Characteristic_polynomial +
, http://dbpedia.org/resource/Geometric_multiplicity +
, http://dbpedia.org/resource/Matrix_%28mathematics%29 +
, http://dbpedia.org/resource/Algebraic_multiplicity +
, http://dbpedia.org/resource/Square_matrix +
, http://dbpedia.org/resource/Diagonalizable_matrix +
, http://dbpedia.org/resource/Normal_matrix +
, http://dbpedia.org/resource/Eigenvalue +
, http://dbpedia.org/resource/Unitary_matrix +
, http://dbpedia.org/resource/Symmetric_matrix +
, http://dbpedia.org/resource/Jordan_matrix +
, http://dbpedia.org/resource/Jordan_normal_form +
, http://dbpedia.org/resource/Matrix_diagonalization +
, http://dbpedia.org/resource/Real_number +
, http://dbpedia.org/resource/Category:Linear_algebra +
, http://dbpedia.org/resource/Root_of_a_polynomial +
|
http://dbpedia.org/property/wikiPageUsesTemplate
|
http://dbpedia.org/resource/Template:Reflist +
, http://dbpedia.org/resource/Template:Matrix_classes +
, http://dbpedia.org/resource/Template:Citation +
, http://dbpedia.org/resource/Template:Use_American_English +
, http://dbpedia.org/resource/Template:Cite_book +
, http://dbpedia.org/resource/Template:Short_description +
|
http://purl.org/dc/terms/subject
|
http://dbpedia.org/resource/Category:Linear_algebra +
|
http://purl.org/linguistics/gold/hypernym
|
http://dbpedia.org/resource/Matrix +
|
http://www.w3.org/ns/prov#wasDerivedFrom
|
http://en.wikipedia.org/wiki/Defective_matrix?oldid=1121771354&ns=0 +
|
http://xmlns.com/foaf/0.1/isPrimaryTopicOf
|
http://en.wikipedia.org/wiki/Defective_matrix +
|
owl:sameAs |
http://www.wikidata.org/entity/Q5251123 +
, http://dbpedia.org/resource/Defective_matrix +
, http://sl.dbpedia.org/resource/Nepopolna_matrika +
, http://ca.dbpedia.org/resource/Matriu_defectiva +
, http://rdf.freebase.com/ns/m.0ddhfd +
, https://global.dbpedia.org/id/4ixLb +
|
rdf:type |
http://dbpedia.org/ontology/AnatomicalStructure +
|
rdfs:comment |
In linear algebra, a defective matrix is a … In linear algebra, a defective matrix is a square matrix that does not have a complete basis of eigenvectors, and is therefore not diagonalizable. In particular, an n × n matrix is defective if and only if it does not have n linearly independent eigenvectors. A complete basis is formed by augmenting the eigenvectors with generalized eigenvectors, which are necessary for solving defective systems of ordinary differential equations and other problems.differential equations and other problems.
, En àlgebra lineal, una matriu defectiva és … En àlgebra lineal, una matriu defectiva és una matriu quadrada que no té una base completa de vectors propis, i és per això no diagonalizable. En particular, una matriu n × n és defectiva si i només si no té n vectors propis linealment independents. Es crea una base completa augmentant els vectors propis amb vectors propis generalitzats, que són necessaris per solucionar sistemes defectius d'equacions diferencials ordinàries i altres problemes.iferencials ordinàries i altres problemes.
|
rdfs:label |
Matriu defectiva
, Defective matrix
|