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In linear algebra, the modal matrix is used in the diagonalization process involving eigenvalues and eigenvectors. Specifically the modal matrix for the matrix is the n × n matrix formed with the eigenvectors of as columns in . It is utilized in the similarity transformation where is an n × n diagonal matrix with the eigenvalues of on the main diagonal of and zeros elsewhere. The matrix is called the spectral matrix for . The eigenvalues must appear left to right, top to bottom in the same order as their corresponding eigenvectors are arranged left to right in .

Attributes	Values
rdf:type	yago:WikicatMatrices yago:Abstraction100002137 yago:Arrangement107938773 yago:Array107939382 yago:Group100031264 yago:Matrix108267640
rdfs:label	Matrice modale (fr) Modal matrix (en)
rdfs:comment	In linear algebra, the modal matrix is used in the diagonalization process involving eigenvalues and eigenvectors. Specifically the modal matrix for the matrix is the n × n matrix formed with the eigenvectors of as columns in . It is utilized in the similarity transformation where is an n × n diagonal matrix with the eigenvalues of on the main diagonal of and zeros elsewhere. The matrix is called the spectral matrix for . The eigenvalues must appear left to right, top to bottom in the same order as their corresponding eigenvectors are arranged left to right in . (en) En algèbre linéaire, la matrice modale est utilisée dans le processus de diagonalisation impliquant des valeurs propres et des vecteurs propres. Plus précisément la matrice modale pour la matrice est la matrice n × n formée avec les vecteurs propres de sous forme de colonnes. Elle est utilisée en diagonalisation (fr)
dcterms:subject	Matrices
Wikipage page ID	17573081 (xsd:integer)
Wikipage revision ID	1084097734 (xsd:integer)
Link from a Wikipage to another Wikipage	John Wiley & Sons Eigenvalues and eigenvectors Generalized eigenvector Linear algebra Matrices Diagonal matrix Jordan normal form Invertible matrix Academic Press Algebraic multiplicity Canonical basis Jordan chain Matrix similarity Diagonalizable Houghton Mifflin Co.
Link from a Wikipage to an external page	https://archive.org/details/firstcourseinlin0000beau
sameAs	Modal matrix Modal matrix Modal matrix Modal matrix Modal matrix
dbp:wikiPageUsesTemplate	dbt:Citation dbt:NumBlk dbt:EquationRef dbt:EquationNote
has abstract	In linear algebra, the modal matrix is used in the diagonalization process involving eigenvalues and eigenvectors. Specifically the modal matrix for the matrix is the n × n matrix formed with the eigenvectors of as columns in . It is utilized in the similarity transformation where is an n × n diagonal matrix with the eigenvalues of on the main diagonal of and zeros elsewhere. The matrix is called the spectral matrix for . The eigenvalues must appear left to right, top to bottom in the same order as their corresponding eigenvectors are arranged left to right in . (en) En algèbre linéaire, la matrice modale est utilisée dans le processus de diagonalisation impliquant des valeurs propres et des vecteurs propres. Plus précisément la matrice modale pour la matrice est la matrice n × n formée avec les vecteurs propres de sous forme de colonnes. Elle est utilisée en diagonalisation où est une matrice diagonale n × n avec les valeurs propres de sur la diagonale principale de et des zéros ailleurs. La matrice s'appelle la matrice spectrale pour . Les valeurs propres doivent apparaître de gauche à droite, de haut en bas dans le même ordre que leurs vecteurs propres correspondants sont disposés de gauche à droite dans . (fr)
prov:wasDerivedFrom	wikipedia-en:Modal_matrix?oldid=1084097734&ns=0
page length (characters) of wiki page	6770 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Modal_matrix
is Link from a Wikipage to another Wikipage of	Modal Generalized eigenvector Jordan normal form Diagonalizable matrix Generalized modal matrix Spectral matrix Modal Matrix (linear algebra) Modal matrix (linear algebra)
is Wikipage redirect of	Generalized modal matrix Spectral matrix Modal Matrix (linear algebra) Modal matrix (linear algebra)
is Wikipage disambiguates of	Modal
is foaf:primaryTopic of	wikipedia-en:Modal_matrix

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