Comprehensive Linear Algebra 3 by Broida & Williamson
Comprehensive Linear Algebra 3 - Table of Contents
6. Polynomials
7. Linear Transformations and Polynomials
8. Canonical Forms
What You Will Learn in Comprehensive Linear Algebra 3
"A Comprehensive Introduction to Linear Algebra (Volume 3: Operators and Tensors)" by "Joel Broida" and "S. G. Williamson" is the most advanced volume in the series. It is designed for students who already have a solid understanding of basic linear algebra and canonical forms. This volume shifts the focus from matrices alone to more abstract structures that appear in higher mathematics and applied sciences.
The book explores "linear operators" in greater depth, helping readers understand how linear transformations act in both finite- and infinite-dimensional spaces. It introduces "linear functionals" and develops the theory in a clear and logical way. A major part of the volume is devoted to "multilinear mappings" and "tensors", which extend linear algebra to multiple inputs and play an important role in physics, engineering, and data analysis.
The later chapters connect these ideas to broader mathematical settings, including inner-product spaces and elements of functional analysis. This makes Volume 3 especially valuable for students preparing for advanced courses or research. Written with precision and clarity, it provides a strong bridge between undergraduate linear algebra and modern mathematical applications.
Book Details & Specifications
Title:
Comprehensive Linear Algebra 3 by Broida & Williamson
Publisher:
Addison-Wesley
Year:
2012
Pages:
303
Type:
PDF
Language:
English
ISBN-10 #:
0201500655
ISBN-13 #:
978-0201500653
License:
CC0 1.0
Amazon:
Amazon
About the Author: Joel Gilbert Broida
The author Joel Gilbert Broida
is a mathematician recognized for his clear and structured writing in "Linear Algebra". His work focuses on explaining advanced topics with logical development, helping students understand abstract ideas such as "Linear Operators" and higher-level algebraic structures. "S. Gill Williamson" is a Professor Emeritus at the University of California, San Diego, with extensive experience in mathematics and computer science. His teaching and research include "Tensors", "Multilinear Maps", and theoretical linear algebra. Together, the authors present complex concepts in a precise yet readable style, supporting advanced undergraduate learning.
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