Introduction to Linear and Matrix Algebra, 1st ed. 2021
Auteur : Johnston Nathaniel
This textbook emphasizes the interplay between algebra and geometry to motivate the study of linear algebra. Matrices and linear transformations are presented as two sides of the same coin, with their connection motivating inquiry throughout the book. By focusing on this interface, the author offers a conceptual appreciation of the mathematics that is at the heart of further theory and applications. Those continuing to a second course in linear algebra will appreciate the companion volume Advanced Linear and Matrix Algebra.
Starting with an introduction to vectors, matrices, and linear transformations, the book focuses on building a geometric intuition of what these tools represent. Linear systems offer a powerful application of the ideas seen so far, and lead onto the introduction of subspaces, linear independence, bases, and rank. Investigation then focuses on the algebraic properties of matrices that illuminate the geometry of the linear transformations that they represent. Determinants, eigenvalues, and eigenvectors all benefit from this geometric viewpoint. Throughout, ?Extra Topic? sections augment the core content with a wide range of ideas and applications, from linear programming, to power iteration and linear recurrence relations. Exercises of all levels accompany each section, including many designed to be tackled using computer software.Introduction to Linear and Matrix Algebra is ideal for an introductory proof-based linear algebra course. The engaging color presentation and frequent marginal notes showcase the author?s visual approach. Students are assumed to have completed one or two university-level mathematics courses, though calculus is not an explicit requirement. Instructors will appreciate the ample opportunities to choose topics that align with the needs of each classroom, and the online homework sets that are available through WeBWorK.
Nathaniel Johnston is an Associate Professor of Mathematics at Mount Allison University in New Brunswick, Canada. His research makes use of linear algebra, matrix analysis, and convex optimization to tackle questions related to the theory of quantum entanglement. His companion volume, Advanced Linear and Matrix Algebra, is also published by Springer.
Motivates the study of linear algebra by exploring the interplay between algebra and geometry
Engages readers with a visual approach that uses color to enhance both content and learning
Features a wide selection of theoretical and applied topics to complement the core material
Incorporates exercises of all levels, including many designed for computer software
Offers corresponding online homework sets through WeBWorK
Includes supplementary material: sn.pub/extras
Date de parution : 05-2022
Ouvrage de 482 p.
17.8x25.4 cm
Disponible chez l'éditeur (délai d'approvisionnement : 15 jours).
Prix indicatif 58,01 €
Ajouter au panierDate de parution : 05-2021
Ouvrage de 482 p.
17.8x25.4 cm
Disponible chez l'éditeur (délai d'approvisionnement : 15 jours).
Prix indicatif 58,01 €
Ajouter au panierThème d’Introduction to Linear and Matrix Algebra :
Mots-clés :
First course in linear algebra textbook; Linear algebra textbook; Matrix algebra textbook; Linear algebra textbook WeBWorK; Matrix algebra vs linear algebra; Vector operations; The dot product; Matrix operations; Linear transformation matrix; Matrix inverses; Subspace linear algebra; Coordinate systems linear algebra; Diagonalization linear algebra; Graph theory introduction; Linear systems; Linear programming; Power iteration PageRank; Google PageRank algorithm; Linear recurrence relations; Geometric approach to linear algebra
