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Linear Algebra de Lina Oliveira

Linear Algebra

Autor Lina Oliveira
en Limba Engleză Paperback – 8 iul 2022
Linear Algebra is intended primarily as an undergraduate textbook but is written in such a way that it can also be a valuable resource for independent learning. The narrative of the book takes a matrix approach: the exposition is intertwined with matrices either as the main subject or as tools to explore the theory. Each chapter contains a description of its aims, a summary at the end of the chapter, exercises, and solutions. The reader is carefully guided through the theory and techniques presented which are outlined throughout in "How to…" text boxes. Common mistakes and pitfalls are also pointed out as one goes along.
Features
  • Written to be self-contained
  • Ideal as a primary textbook for an undergraduate course in linear algebra
  • Applications of the general theory which are of interest to disciplines outside of mathematics, such as engineering
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Specificații

ISBN-13: 9780815373315
ISBN-10: 0815373317
Pagini: 328
Ilustrații: 22 Line drawings, black and white; 22 Illustrations, black and white
Dimensiuni: 156 x 234 x 18 mm
Greutate: 0.49 kg
Ediția:1
Editura: CRC Press
Colecția Chapman and Hall/CRC

Public țintă

Academic

Cuprins

1. Matrices. 1.1. Real and Complex Matrices. 1.2. Matrix Calculus. 1.3. Matrix Inverses. 1.4. Elementary Matrices. 1.5. Exercises. 1.6. At a Glance. 2. Determinant. 2.1. Axiomatic Definition. 2.2. Leibniz's Formula. 2.3. Laplace's Formula. 2.4. Exercises. 2.5. At a Glance. 3. Vector Spaces. 3.1. Vector Spaces. 3.2. Linear Independence. 3.3. Bases and Dimension. 3.4. Null Space, Row Space and Column Space. 3.5. Sum and intersection of Subspaces. 3.6. Change of Basis. 3.7. Exercises. 3.8. At a Glance. 4. Eigenvalues and Eigenvectors. 4.1. Spectrum of a Matrix. 4.2. Spectral Properties. 4.3. Similarity and Diagonalisation. 4.4. Jordan Canonical Form. 4.5. Exercises. 4.6. At a Glance. 5. Linear Transformations. 5.1. Linear Transformations. 5.2. Matrix Representations. 5.3. Null Space and Image. 5.4. Isomorphisms and Rank-Nullity Theorem. 5.5. Composition and Invertibility. 5.6. Change of Basis. 5.7. Spectrum and Diagonalisation. 5.8. Exercises. 5.9. At a Glance. 6. Inner Product Spaces. 6.1. Real Inner Product Spaces. 6.2. Complex Inner Product Spaces. 6.3. Orthogonal Sets. 6.4. Orthogonal and Unitary Diagonalisation. 6.5. Singular Value decomposition. 6.6. Affine Subspaces of Rn. 6.7. Exercises. 6.8. At a Glance. 7 Special Matrices by Example. 7.1. Least Squares Solutions. 7.2. Markov Chains. 7.3. Population Dynamics. 7.4. Graphs. 7.5. Differential Equations. 7.6. Exercises. 7.7. At a Glance. 8. Appendix. 8.1. Uniqueness of Reduced Row Echelon Form. 8.2. Uniqueness of determinant. 8.3. Direct sum of Subspaces. 9. Solutions.

Notă biografică

Lina Oliveira earned her DPhil in Mathematics from the University of Oxford, UK and is a faculty member of the Department of Mathematics of Instituto Superior T□ecnico, University of Lisbon, Portugal. She has taught several graduate and undergraduate courses at Instituto Superior T□ecnico where she regularly teaches Linear Algebra since 2001. Her research interests are in the areas of Functional Analysis, Operator Algebras and Operator Theory. She is currently the head of the Linear Algebra course at the portuguese Air Force Academy.

Recenzii

Linear Algebra by mathematician Lina Oliveira is intended primarily as an undergraduate textbook but is written in such a way that it can also be a valuable resource for independent learning as well. Exceptional in organization and presentation, Linear Algebra is unreservedly recommended for personal, community, and academic library Applied Mathematics, Albegra and Trigonometry collections and curriculums.
- Midwest Book Review

Descriere

This book is intended primarily as an undergraduate textbook but is written in such a way that it can be also a valuable resource for independent learning. The narrative of the book takes a matrix approach: the exposition is intertwined with matrices either as the main subject or as tools to explore the theory.