This book is based on a course for first-semester science students, held by the second author at the University of Zurich several times. Its goal is threefold: to have students learn a minimal working knowledge of linear algebra, acquire some computational skills, and familiarize them with mathematical language to make mathematical literature more accessible. Therefore, we give precise definitions, introduce helpful notations, and state any results carefully worded. We provide no proofs of these results but typically illustrate them with numerous examples. Additionally, for better understanding, we often give supporting arguments for why they are valid.
Author(s): Manuel Benz; Thomas Kappeler
Series: UNITEXT, 151
Edition: 1
Publisher: Springer International Publishing
Year: 2023
Language: English
Commentary: https://link.springer.com/book/10.1007/978-3-031-27220-2
Pages: 259
City: Zurich, Switzerland
Tags: Linear Algebra, Algebra
Preface
Addendum
Contents
1 Systems of Linear Equations
1.1 Introduction
1.2 Systems with Two Equations and Two Unknowns
Problems
1.3 Gaussian Elimination
Problems
2 Matrices and Related Topics
2.1 Matrices
Problems
2.2 Linear Dependence, Bases, Coordinates
Problems
2.3 Determinants
Problems
3 Complex Numbers
3.1 Complex Numbers: Definition and Operations
Problems
3.2 The Fundamental Theorem of Algebra
Problems
3.3 Linear Systems with Complex Coefficients
Problems
4 Vector Spaces and Linear Maps
4.1 Vector Spaces
Problems
4.2 Linear Maps
Problems
4.3 Inner Products
Inner Products on R-Vector Spaces
Isometries and Orthogonal Matrices
Inner Products on C-Vector Spaces
Vector Product in R3
Problems
5 Eigenvalues and Eigenvectors
5.1 Eigenvalues and Eigenvectors of C-Linear Maps
Problems
5.2 Eigenvalues and Eigenvectors of R-Linear Maps
Problems
5.3 Quadratic Forms on Rn
Problems
6 Differential Equations
6.1 Introduction
6.2 Linear ODEs with Constant Coefficients of First Order
Problems
6.3 Linear ODEs with Constant Coefficients of Higher Order
Problems
Solutions
Solutions of Problems of Sect.1.2
Solutions of Problems of Sect.1.3
Solutions of Problems of Sect.2.1
Solutions of Problems of Sect.2.2
Solutions of Problems of Sect.2.3
Solutions of Problems of Sect.3.1
Solutions of Problems of Sect.3.2
Solutions of Problems of Sect.3.3
Solutions of Problems of Sect.4.1
Solutions of Problems of Sect.4.2
Solutions of Problems of Sect.4.3
Solutions of Problems of Sect.5.1
Solutions of Problems of Sect.5.2
Solutions of Problems of Sect.5.3
Solutions of Problems of Sect.6.2
Solutions of Problems of Sect.6.3
Reference
Index
