Mello Invitation to Linear Algebra

1. Auflage 2017
ISBN: 978-1-4987-7957-9
Verlag: CRC Press
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 408 Seiten

Reihe: Textbooks in Mathematics

Unlike most books of this type, the book has been organized into “lessons” rather than chapters. This has been done to limit the size of the mathematical morsels that students must digest during each class, and to make it easier for instructors to budget class time. The book contains considerably more material than normally appears in a first course. For example, several advanced topics such as the Jordan canonical form and matrix power series have been included. This was done to make the book more flexible than most books presently available, and to allow instructors to choose enrichment material which may reflect their interests, and those of their students.

Autoren/Hrsg.

Mello, David C.

Fachgebiete

• Mathematik | Informatik Mathematik Algebra
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle

Inhaltsverzeichnis

Matrices and Linear Systems

Introduction to Matrices

Matrix Multiplication

Additional Topics in Matrix Algebra

Introduction to Linear Systems

The Inverse of a Matrix

Determinants

Introduction to Determinants

Properties of Determinants

Applications of Determinants

A First Look at Vector Spaces

Introduction to Vector Spaces

Subspaces of Vector Spaces

Linear Dependence and Independence

Basis and Dimension

The Rank of a Matrix

Linear Systems Revisited

More About Vector Spaces

Sums and Direct Sums of Subspaces

Quotient Spaces

Change of Basis

Euclidean Spaces

Orthonormal Bases

Linear Transformations

Introduction to Linear Transformations

Isomorphisms of Vector Spaces

The Kernel and Range of a Linear Transformation

Matrices of Linear Transformations

Similar Matrices

Matrix Diagonalization

Eigenvalues and Eigenvectors

Diagonalization of Square Matrices

Diagonalization of Symmetric Matrices

Complex Vector Spaces

Complex Vector Spaces

Unitary and Hermitian Matrices

Advanced Topics

Powers of Matrices

Functions of a Square Matrix

Matrix Power Series

Minimal Polynomials

Direct Sum Decompositions

Jordan Canonical Form

Applications

Systems of First Order Differential Equations

Stability Analysis of First Order Systems

Coupled Oscillations

Appendix

Solutions and Hints to Selected Exercises

Über Autor(innen)

David C. Mello received an M.A. degree in Mathematics from Rhode Island College, and both M.S. and Ph.D. degrees in Applied Mathematics from Brown University. He is currently Professor of Mathematics, Department of Mathematics, Johnson & Wales University, Providence, Rhode Island. He has taught college-level mathematics for more than 30 years.