Rita Fioresi, Marta Morigi

Introduction to Linear Algebra

• Broschiertes Buch

Produktbeschreibung

This book offers a straightforward introduction to linear algebra that requires a minimal mathematical background to read and engage with and is primarily aimed at students in applied fields (e.g. Computer Science and Engineering), providing them with a concrete, rigorous approach to face and solve various types of problems.

Produktdetails

• Verlag: Taylor & Francis Ltd (Sales)
• Seitenzahl: 274
• Erscheinungstermin: 25. September 2023
• Englisch
• Abmessung: 254mm x 178mm x 15mm
• Gewicht: 481g
• ISBN-13: 9780367635503
• ISBN-10: 036763550X
• Artikelnr.: 68712116

Autorenporträt

Rita Fioresi and Marta Morigi are professors at the University of Bologna and teach linear algebra courses to students of all majors. Their research publications are centered into algebra with some applications (R. Fioresi Lie theory & machine learning, M. Morigi Group theory).

Inhaltsangabe

1. Introduction to Linear Systems. 1.1. Linear systems: First Examples.
1.2. Matrices. 1.3. Matrices and Linear Systems. 1.4. The Gaussian
Algorithm. 1.5. Exercises with Solutions. 1.6. Suggested Exercises. 2.
Vector Spaces. 2.1. Introduction: The Set of Real Numbers. 2.2. The Vector
Space Rn and the Vector Space of Matrices. 2.3. Vector Spaces. 2.4.
SubSpaces. 2.5. Exercises with Solutions. 2.6. Suggested Exercises. 3.
Linear Combination and Linear Independence. 3.1. Linear Combinations and
Generators. 3.2. Linear Independence. 3.3. Exercises with Solutions. 3.4.
Suggested Exercises. 4. Basis and Dimension. 4.1. Basis: Definition and
Examples. 4.2. The Concept of Dimension. 4.3. Gaussian Algorithm. 4.4.
Exercises with Solutions. 4.5. Suggested Exercises. 4.6. Appendix: The
Completion Theorem. 5. Linear Transformations. 5.1. Linear Transformations:
Definition. 5.2. Linear Maps and Matrices. 5.3. the Composition of Linear
transformations. 5.4. Kernel and Image. 5.5. The Rank Nullity Theorem. 5.6.
Isomorphism of Vector Spaces. 5.7. Calculation of Kernel and Image. 5.8.
Exercises with Solutions. 5.9. Suggested Exercises. 6. Linear Systems.
6.1. Preimage. 6.2. Linear Systems. 6.3. Exercises with Solutions. 6.4.
Suggested Exercises. 7. Determinant and Inverse. 7.1. Definition of
Determinant. 7.2. Calculating the Determinant: Cases 2 _ 2 and 3 _ 3. 7.3.
Calculating the Determinant with a Recursive Method. 7.4. Inverse of a
Matrix. 7.5. Calculation of the Inverse with the Gaussian Algorithm. 7.6.
The Linear Maps from Rn to Rn. 7.7. Exercises with Solutions. 7.8.
Suggested Exercises. 7.9. Appendix. 8. Change of Basis. 8.1. Linear
Transformations and Matrices. 8.2. The Identity Map. 8.3. Change of Basis
for Linear Transformations. 8.4. Exercises with Solutions. 8.5. Suggested
Exercises. 9. Eigenvalues and Eigenvectors. 9.1. Diagonalizability. 9.2.
Eigenvalues and Eigenvectors. 9.3. Exercises with Solutions. 9.4. Suggested
Exercises. 10. Scalar Products. 10.1. Bilinear Forms. 10.2. Bilinear Forms
and Matrices. 10.3. Basis Change. 10.4. Scalar Products. 10.5. Orthogonal
Subspaces. 10.6. Gram-Schmidt Algorithm. 10.7. Exercises with Solutions.
10.8. Suggested Exercises. 11. Spectral Theorem. 11.1. Orthogonal Linear
Transformations. 11.2. Orthogonal Matrices. 11.3. Symmetric Linear
Transformations. 11.4. The Spectral Theorem. 11.5. Exercises with
Solutions. 11.6. Suggested Exercises. 11.7. Appendix: The Complex Case.
12. Applications of Spectral Theorem and Quadratic Forms. 12.1.
Diagonalization of Scalar Products. 12.2. Quadratic Forms. 12.3. Quadratic
Forms and in the Plane. 12.4. Exercises with Solutions. 12.5. Suggested
Exercises. 13. Lines and Planes. 13.1. Points and Vectors in R3. 13.2.
Scalar Product and Vector Product. 13.3. Lines in R3. 13.4. Planes in R3.
13.5. Exercises with Solutions. 13.6. Suggested Exercises. 14. Introduction
to Modular Arithmetic. 14.1. The Principle of Induction. 14.2. The Division
Algorithm and Euclid's Algorithm. 14.3. Congruence Classes. 14.4.
Congruences. 14.5. Exercises with Solutions. 14.6. Suggested Exercises.
14.7. Appendix: Elementary Notions of Set Theory. Appendix A. Complex
Numbers. A.1. Complex Numbers. A.2. Polar Representation. Appendix B.
Solutions of Some Suggested Exercises. Bibliography. Index