A concise text on advanced linear algebra

This engaging textbook for advanced undergraduate students and beginning graduates covers the core subjects in linear algebra. The author motivates the concepts by drawing clear links to applications and other important areas, such as differential topology and quantum mechanics. The book places particular emphasis on integrating ideas from analysis wherever appropriate. For example, the notion of determinant is shown to appear from calculating the index of a vector field which leads to a self-contained proof of the Fundamental Theorem of Algebra, and the Cayley-Hamilton theorem is established by recognizing the fact that the set of complex matrices of distinct eigenvalues is dense. The material is supplemented by a rich collection of over 350 mostly proof-oriented exercises, suitable for students from a wide variety of backgrounds. Selected solutions are provided at the back of the book, making it suitable for self-study as well as for use as a course text Read more... Abstract: This engaging textbook for advanced undergraduate students and beginning graduates covers the core subjects in linear algebra. The author motivates the concepts by drawing clear links to applications and other important areas, such as differential topology and quantum mechanics. The book places particular emphasis on integrating ideas from analysis wherever appropriate. For example, the notion of determinant is shown to appear from calculating the index of a vector field which leads to a self-contained proof of the Fundamental Theorem of Algebra, and the Cayley-Hamilton theorem is established by recognizing the fact that the set of complex matrices of distinct eigenvalues is dense. The material is supplemented by a rich collection of over 350 mostly proof-oriented exercises, suitable for students from a wide variety of backgrounds. Selected solutions are provided at the back of the book, making it suitable for self-study as well as for use as a course text This Engaging Textbook For Advanced Undergraduate Students And Beginning Graduates Covers The Core Subjects In Linear Algebra. The Author Motivates The Concepts By Drawing Clear Links To Applications And Other Important Areas, Such As Differential Topology And Quantum Mechanics. The Book Places Particular Emphasis On Integrating Ideas From Analysis Wherever Appropriate. For Example, The Notion Of Determinant Is Shown To Appear From Calculating The Index Of A Vector Field Which Leads To A Self-contained Proof Of The Fundamental Theorem Of Algebra, And The Cayley-hamilton Theorem Is Established By Recognizing The Fact That The Set Of Complex Matrices Of Distinct Eigenvalues Is Dense. The Material Is Supplemented By A Rich Collection Of Over 350 Mostly Proof-oriented Exercises, Suitable For Students From A Wide Variety Of Backgrounds. Selected Solutions Are Provided At The Back Of The Book, Making It Suitable For Self-study As Well As For Use As A Course Text. --provided By Publisher. Vector Spaces -- Linear Mappings -- Determinants -- Scalar Products -- Real Quadratic Forms And Self-adjoint Mappings -- Complete Quadratic Forms And Self-adjoint Mappings -- Jordan Decompositions -- Selected Topis -- Excursion: Quantum Mechanics In A Nutshell. Yisong Yang, Polytechnic School Of Engineering, New York University. Includes Bibliographical References And Index. Main subject categories: • Linear algebra • Vector spaces • Linear mappings • Determinants • Scalar products • Real quadratic forms and self-adjoint mappings • Complex quadratic forms and self-adjoint mappings • Jordan decomposition • Quantum mechanicsThis engaging textbook for advanced undergraduate students and beginning graduates covers the core subjects in linear algebra. The author motivates the concepts by drawing clear links to applications and other important areas, such as differential topology and quantum mechanics.The book places particular emphasis on integrating ideas from analysis wherever appropriate. For example, the notion of determinant is shown to appear from calculating the index of a vector field which leads to a self-contained proof of the Fundamental Theorem of Algebra, and the Cayley‒Hamilton theorem is established by recognizing the fact that the set of complex matrices of distinct eigenvalues is dense.The material is supplemented by a rich collection of over 350 mostly proof-oriented exercises, suitable for students from a wide variety of backgrounds. Selected solutions are provided at the back of the book, making it suitable for self-study as well as for use as a course text. An engaging textbook for advanced undergraduate students and beginning graduates covering the core subjects in linear algebra. The author clearly motivates the theory to give readers a thorough grasp of the concepts and draws clear links to applications in mathematics and beyond.