Linear Algebra by Jason Siefken
Linear Algebra - Table of Contents
- 1. Sets, Vectors, and Notation
- 2. Sets of Vectors, Lines, and Planes
- 3. Spans, Translated Spans & Independence
- 4. Dot Products and Normal Forms
- 5. Projections and Vector Components
- 6. Subspaces and Bases
- 7. Matrix Systems of Linear Equations
- 8. Coordinates and Change of Basis I
- 9. Linear Transformations and Maps
- 10. Composition of Linear Transformations
- 11. Range and Nullspace (Kernel/Image)
- 12. Inverse Functions and Inverse Matrices
- 13. Change of Basis II
- 14. Determinants and Properties
- 15. Eigenvalues and Eigenvectors
- 16. Diagonalization and Spectral Analysis
What You Will Learn in Linear Algebra
Linear Algebra by Jason Siefken is an authoritative, open-access undergraduate textbook that provides students with a visually intuitive, proof-supported foundation in core vector space and matrix theory. This comprehensive volume guides readers through vector notation, line and plane geometry, spans and linear dependence, dot product normal forms, vector projections, subspace bases, matrix-system representations, coordinate basis changes, linear transformations, image and kernel spaces, matrix inversion, determinants, eigenvalues, and matrix diagonalization with exceptional pedagogical clarity and logical precision.
Designed for undergraduate mathematics majors, computer science students, engineering practitioners, and data science learners, this foundational text bridges concrete geometric intuition directly with formal algebraic proof structures. Siefken details step-by-step formulations for calculating subspace dimensions, finding change-of-basis matrices, computing kernel bases, evaluating transformation compositions, and diagonalizing symmetric matrices. Whether you are building background for multivariable calculus, machine learning algorithms, or differential equation systems, this book offers an indispensable roadmap.
Recognized globally for its clear sequence and accessible approach to abstract concepts, it stands as one of the best introductory textbooks for mastering vector spaces and linear transformations. By unifying geometric projections directly with matrix operators and spectral decomposition, it serves as an essential tool for learning linear algebra with confidence.
Book Details & Specifications
Title:
Linear Algebra by Jason Siefken
Publisher:
Jason Siefken
Year:
2020
Pages:
219
Type:
PDF
Language:
English
ISBN-10 #:
N\A
ISBN-13 #:
N\A
License:
CC BY-SA 4.0
Amazon:
Amazon
About the Author: Jason Siefken
The author Jason Siefken
is a mathematician and university educator known for his strong focus on "Mathematics Education" and student-centered teaching. He teaches at the "University of Toronto", where he works closely with undergraduate students in courses such as "Linear Algebra" and differential equations. As the author of "Linear Algebra", he emphasizes "Inquiry-Based Learning", encouraging students to explore ideas through guided problems and discussion. His teaching philosophy prioritizes "Conceptual Understanding" over memorization, helping learners develop intuition about vectors, matrices, and linear systems through active engagement and clear mathematical thinking.
Read or Downloadable Linear Algebra
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