Comprehensive Linear Algebra 2 by Broida & Williamson
Comprehensive Linear Algebra 2 - Table of Contents
- 9. Linear Forms, Dual Spaces, and Annihilators
- 10. Linear Operators, Adjoints, and Spectral Theory
- 11. Multilinear Mappings and Tensor Algebras
- 12. Hilbert Spaces, Inner Products, and Completeness
What You Will Learn in Comprehensive Linear Algebra 2
A Comprehensive Introduction to Linear Algebra (Volume 2) by Joel G. Broida and S. Gill Williamson is an authoritative, mathematically rigorous graduate-level textbook published by Addison-Wesley that provides an in-depth treatment of duality, advanced operator theory, and inner product function spaces. Building upon foundational vector space theory, this comprehensive volume guides readers through linear functionals, dual bases, annihilators, adjoint operators, spectral decomposition, multilinear maps, tensor products, contraction operations, and infinite-dimensional Hilbert space operators with exceptional logical rigor and mathematical depth.
Designed for graduate mathematics majors, theoretical physicists, quantum mechanics researchers, and functional analysts, this foundational text bridges finite-dimensional matrix analysis with infinite-dimensional operator theory. Broida and Williamson detail step-by-step proofs for dual space isomorphisms, normal operator spectral theorems, tensor algebra constructions, and orthonormal Hilbert space completeness conditions. Whether you are studying quantum state mechanics, preparing for advanced qualifying examinations, or researching differential geometry tensor fields, this book offers an indispensable roadmap.
Recognized globally as a definitive text on advanced linear algebra and multilinear structures, it stands as one of the best reference books for linear operators, tensor analysis, and Hilbert space geometry. By connecting dual space pairings directly to tensor product spaces and Hilbert operator mechanics, it serves as an essential tool for mastering advanced linear algebra with confidence.
Book Details & Specifications
Title:
Comprehensive Linear Algebra 2 by Broida & Williamson
Publisher:
Addison-Wesley
Year:
2012
Pages:
217
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
and Samuel Gill Williamson are distinguished professors and researchers in mathematics and computer science at the University of California, San Diego (UCSD), internationally acclaimed for their research in combinatorics, linear algebra, and mathematical physics.
Through A Comprehensive Introduction to Linear Algebra (Volume 2), Broida and Williamson deliver a masterfully structured, rigorous presentation of advanced linear analysis. Their detailed proof structures, explicit algebraic derivations, and balanced focus on tensor algebra and functional analysis make this text a classic reference for linear operators and multilinear tensor analysis valued by mathematicians worldwide.
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