Linear Algebra Volume 03: Spectrum, Eigenvalues and Orthogonal Operators (Graduate Mathematics Book 6)
English | April 29, 2026 | ASIN: B0GYWPX31Y | 390 pages | PDF | 9.27 MB
Linear Algebra, Volume 03: Spectrum, Eigenvalues, and Orthogonal Operators is an advanced academic text designed for students, teachers, and professionals who want to deepen their understanding of modern linear algebra.This volume focuses on the spectral structure of linear operators, developing the theory of eigenvalues, eigenvectors, invariant subspaces, characteristic polynomials, diagonalization, the Spectral Theorem, Singular Value Decomposition, positive operators, polar decomposition, and orthogonal transformations.With a rigorous yet progressive approach, the book connects algebraic methods with geometric intuition, helping readers understand how linear operators act on vector spaces and how their structure can be analyzed through eigenvalues, eigenspaces, orthogonal bases, and decompositions.Inside this volume, readers will find:Clear definitions and theoretical foundationsDetailed propositions, theorems, and proofsWorked examples and solved exercisesProposed exercises for independent practiceApplications in physics, engineering, data analysis, optimization, numerical methods, and scientific computingHistorical references to major figures such as John von Neumann, Marshall Stone, and Joseph-Louis LagrangeThis book is especially useful for advanced undergraduate and graduate students in mathematics, physics, engineering, computer science, and related scientific fields. It is also suitable as a reference text for instructors, researchers, and independent learners interested in spectral theory and the deeper structure of linear transformations.Part of the Postgraduate Mathematics Series, this volume offers a solid bridge between theoretical rigor and applied mathematical reasoning, supporting the reader in the study of advanced linear algebra and its applications across modern science and technology.
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