Exam Preparation Linear Algebra

Volume I: Matrices, Determinants, Linear Equation Systems, Vector Spaces, Linear Transformations, Eigenvalues and Eigenvectors
2. Auflage 2026
ISBN: 978-3-032-38360-0
Verlag: Springer

Buch, Englisch, Format (B × H): 155 mm x 235 mm

Reihe: Mathematics Study Resources

This book is the ideal companion for all undergraduate students studying mathematics, as well as for foundational courses in engineering, natural sciences, and economics. It is especially suitable for preparing for assessment exams and basic foundational exams in the area of linear algebra.

Volume I covers the following central topics:

• Matrices and Determinants
• Linear Systems of Equations
• Vector Spaces
• Linear Transformations
• Eigenvalues and Eigenvectors

The material is not presented in the traditional textbook format of definition, theorem, and proof. Instead, it can be learned and practiced through more than 600 exercises of varying difficulty levels. All exercises are worked out step by step, with clear explanations of the solution process and many practical calculation tips. A wide range of typical (exam-style) problems is included. At the end, 150 multiple-choice questions and 4 complete sample exams with detailed solutions give readers the opportunity to test their knowledge and consolidate the material.

Zielgruppe

Lower undergraduate

Autoren/Hrsg.

Michaels, Thomas C. T.

Liechti, Marcel

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Reelle Analysis
• Mathematik | Informatik Mathematik Mathematik Allgemein
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Mathematik | Informatik Mathematik Algebra

Inhaltsverzeichnis

Part I. Fundamentals: Matrices and linear systems of equations.- Chapter 1. Matrices.- Chapter 2. Systems of Linear Equations.- Chapter 3. Determinants.- Chapter 4. LR Decomposition.-Part II. Vector spaces.- Chapter 5. Vector Spaces and Subspaces.- Chapter 6. Vector Space Structure: Basis, Dimension and Coordinates.- Part III. Linear mappings.- Chapter 7. Linear Mappings I: Definition and Matrix Representation.- Chapter 8. Linear Mappings II: Kernel, Image and Basis Change.- Chapter 9. Eigenvalues and Eigenvectors.- Chapter 10. Practice Questions and Sample Exams.

Über Autor(innen)

Thomas C. T. Michaels is Professor of at ETH Zurich. His research group focuses on the mathematical modelling of complex biological processes, in particular those associated with disease. He was born in Lugano and studied physics and mathematics at ETH Zurich. He obtained his doctorate in biophysics from the University of Cambridge and has worked as a lecturer and researcher at Harvard University, the University of Cambridge and University College London.

Marcel Liechti is a former upper-secondary (gymnasium) mathematics teacher and a curriculum developer in computer science. He founded and ran a start-up company for 25 years. For more than 20 years, he has been actively involved as a mathematics coach preparing students for assessment and foundation examinations at Swiss universities, including ETH Zurich, the University of Zurich, and the University of St. Gallen.