November 2024
Intermediate to advanced
328 pages
9h 21m
French
Content preview from Algèbre linéaire pratique pour la science des données
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Chapitre 9. Matrices orthogonales et décomposition QR
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Tu apprendras cinq grandes décompositions dans ce livre : la décomposition vectorielle orthogonale, la décomposition QR, la décomposition LU, l'eigendecomposition et la décomposition des valeurs singulières. Ce ne sont pas les seules décompositions en algèbre linéaire, mais ce sont les plus importantes pour la science des données et l'apprentissage automatique.
Dans ce chapitre, tu apprendras à connaître la matrice QR. Et en cours de route, tu apprendras un nouveau type spécial de matrice (orthogonale). La décomposition QR est un outil de travail qui permet de réaliser des applications telles que l'inverse de la matrice, l'ajustement du modèle des moindres carrés et la décomposition de l'égide. Par conséquent, comprendre et se familiariser avec la décomposition QR t'aidera à améliorer tes compétences en algèbre linéaire.
Matrices orthogonales
Je vais commencer par te présenter les matrices orthogonales. Une matrice orthogonale est une matrice spéciale qui est importante pour plusieurs décompositions, notamment la décomposition QR, la décomposition de l'égide et la décomposition des valeurs singulières. La lettre est souvent utilisée pour indiquer les matrices orthogonales. Les matrices orthogonales ont deux propriétés :
- Colonnes orthogonales
-
Toutes les colonnes sont orthogonales par paire. ...
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