Algèbre Linéaire: espaces vectoriels, matrices et applications

Name: Algèbre Linéaire: espaces vectoriels, matrices et applications
Brand: Independently Published
SKU: 9798257910753
Price: 3170.0 INR
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by Alessio Mangoni

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ISBN13: 9798257910753
Binding: Paperback
Subject: N/A
Publisher: Independently Published
Publisher Imprint: Independently Published
Publication Date: April 18, 2026
Pages: 450
Original Price: USD 29.4
Language: French
Edition: N/A
Item Weight: 713 grams
BISAC Subject(s): NON-CLASSIFIABLE

About The Book

L'acquisition d'une ma�trise solide de l'alg�bre lin�aire requiert avant tout la compr�hension des structures qui en constituent le fondement. Le pr�sent volume se propose de d�velopper cette compr�hension � travers un expos� qui allie rigueur th�orique et attention aux aspects op�rationnels. Chaque chapitre propose des exercices, enti�rement r�solus dans une section finale sp�cialement consacr�e du livre.

Le traitement d�veloppe de mani�re organique l'ensemble du programme d'un cours universitaire d'alg�bre lin�aire. On part des fondements op�rationnels: syst�mes d'�quations lin�aires, �limination de Gauss, calcul matriciel et th�orie du d�terminant. On construit ensuite le coeur conceptuel de la mati�re: la d�finition axiomatique d'espace vectoriel, le th�or�me de Steinitz, la notion de base et de dimension, la formule de Grassmann. Les applications lin�aires traduisent ces structures dans le langage des matrices associ�es et du changement de base. Les chapitres suivants abordent valeurs propres, diagonalisation et leurs applications, puissances de matrices, suites r�currentes, syst�mes diff�rentiels, pour ensuite d�velopper la th�orie du produit scalaire, les espaces euclidiens, le proc�d� de Gram-Schmidt et le th�or�me spectral pour les matrices sym�triques r�elles. Le volume se conclut avec les formes bilin�aires et quadratiques, la classification des coniques et des quadriques, et la forme canonique de Jordan avec l'exponentielle de matrice.

Le parcours est structur� de mani�re s�quentielle et progressive: chaque chapitre utilise le mat�riel des pr�c�dents et introduit de nouveaux concepts avec progressivit�. Chaque r�sultat important est d�montr�; chaque d�finition est suivie d'exemples r�solus et, lorsque c'est possible, d'une figure qui en rend visible la signification g�om�trique. Les observations diss�min�es dans le texte signalent les erreurs les plus fr�quentes et les subtilit�s qu'il est facile de n�gliger lors d'une premi�re lecture. Les exercices de fin de chapitre permettent de consolider ce qui a �t� appris et de v�rifier la compr�hension. Le livre ne pr�suppose que les math�matiques de premi�re ann�e universitaire, ensembles, fonctions, trigonom�trie �l�mentaire, et ne requiert aucun pr�requis en alg�bre lin�aire. Il est con�u pour les �tudiants de Math�matiques, Physique, Ing�nierie et Informatique qui souhaitent construire une comp�tence solide dans cette mati�re.

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