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Modal matrix Matrice modale
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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 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 .
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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 . 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 .
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