{"product_id":"linear-algebra-and-its-applications-2e-functional-analysis-set-isbn-9780470555545","title":"Linear Algebra and Its Applications, 2e + Functional Analysis Set","description":"\u003cp\u003eThis set features: \u003ci\u003eLinear Algebra and Its Applications, Second Edition\u003c\/i\u003e (978-0-471-75156-4) and \u003ci\u003eFunctional Analysis\u003c\/i\u003e (978-0-471-55604-6) both by Peter D. Lax.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e\u003ci\u003eLinear Algebra and Its Applications, Second Edition\u003c\/i\u003e (978-0-471-75156-4)\u003c\/b\u003e\u003cbr\u003e\u003ci\u003eLinear Algebra and Its Applications\u003c\/i\u003e, Second Edition presents linear algebra as the theory and practice of linear spaces and linear maps with a unique focus on the analytical aspects as well as the numerous applications of the subject. In addition to thorough coverage of linear equations, matrices, vector spaces, game theory, and numerical analysis, the Second Edition features student-friendly additions that enhance the book's accessibility, including expanded topical coverage in the early chapters, additional exercises, and solutions to selected problems.\u003c\/p\u003e \u003cp\u003eBeginning chapters are devoted to the abstract structure of finite dimensional vector spaces, and subsequent chapters address convexity and the duality theorem as well as describe the basics of normed linear spaces and linear maps between normed spaces.\u003c\/p\u003e \u003cp\u003eFurther updates and revisions have been included to reflect the most up-to-date coverage of the topic, including:\u003c\/p\u003e \u003cul\u003e \u003cli\u003eThe QR algorithm for finding the eigenvalues of a self-adjoint matrix\u003c\/li\u003e \u003cli\u003eThe Householder algorithm for turning self-adjoint matrices into tridiagonal form\u003c\/li\u003e \u003cli\u003eThe compactness of the unit ball as a criterion of finite dimensionality of a normed linear space\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003eAdditionally, eight new appendices have been added and cover topics such as: the Fast Fourier Transform; the spectral radius theorem; the Lorentz group; the compactness criterion for finite dimensionality; the characterization of commentators; proof of Liapunov's stability criterion; the construction of the Jordan Canonical form of matrices; and Carl Pearcy's elegant proof of Halmos' conjecture about the numerical range of matrices.\u003c\/p\u003e \u003cp\u003eClear, concise, and superbly organized, Linear Algebra and Its Applications, Second Edition serves as an excellent text for advanced undergraduate- and graduate-level courses in linear algebra. Its comprehensive treatment of the subject also makes it an ideal reference or self-study for industry professionals.\u003c\/p\u003e \u003cp\u003e\u003cb\u003e\u003ci\u003eFunctional Analysis\u003c\/i\u003e (978-0-471-55604-6)\u003c\/b\u003e\u003c\/p\u003e \u003cul\u003e \u003cli\u003eIncludes sections on the spectral resolution and spectral representation of self adjoint operators, invariant subspaces, strongly continuous one-parameter semigroups, the index of operators, the trace formula of Lidskii, the Fredholm determinant, and more.\u003c\/li\u003e \u003cli\u003eAssumes prior knowledge of Naive set theory, linear algebra, point set topology, basic complex variable, and real variables.\u003c\/li\u003e \u003cli\u003eIncludes an appendix on the Riesz representation theorem.\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003e\u003ci\u003e\u003cb\u003eLinear Algebra and Its Applications, 2nd Edition\u003c\/b\u003e\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003ePreface.\u003c\/p\u003e \u003cp\u003ePreface to the First Edition.\u003c\/p\u003e \u003cp\u003e1. Fundamentals.\u003c\/p\u003e \u003cp\u003e2. Duality.\u003c\/p\u003e \u003cp\u003e3. Linear Mappings.\u003c\/p\u003e \u003cp\u003e4. Matrices.\u003c\/p\u003e \u003cp\u003e5. Determinant and Trace.\u003c\/p\u003e \u003cp\u003e6. Spectral Theory.\u003c\/p\u003e \u003cp\u003e7. Euclidean Structure.\u003c\/p\u003e \u003cp\u003e8. Spectral Theory of Self-Adjoint Mappings.\u003c\/p\u003e \u003cp\u003e9. Calculus of Vector- and Matrix-Valued Functions.\u003c\/p\u003e \u003cp\u003e10. Matrix Inequalities.\u003c\/p\u003e \u003cp\u003e11. Kinematics and Dynamics.\u003c\/p\u003e \u003cp\u003e12. Convexity.\u003c\/p\u003e \u003cp\u003e13. The Duality Theorem.\u003c\/p\u003e \u003cp\u003e14. Normed Linear Spaces.\u003c\/p\u003e \u003cp\u003e15. Linear Mappings Between Normed Linear Spaces.\u003c\/p\u003e \u003cp\u003e16. Positive Matrices.\u003c\/p\u003e \u003cp\u003e17. How to Solve Systems of Linear Equations.\u003c\/p\u003e \u003cp\u003e18. How to Calculate the Eigenvalues of Self-Adjoint Matrices.\u003c\/p\u003e \u003cp\u003e19. Solutions.\u003c\/p\u003e \u003cp\u003eBibliography.\u003c\/p\u003e \u003cp\u003eAppendix 1. Special Determinants.\u003c\/p\u003e \u003cp\u003eAppendix 2. The Pfaffian.\u003c\/p\u003e \u003cp\u003eAppendix 3. Symplectic Matrices.\u003c\/p\u003e \u003cp\u003eAppendix 4. Tensor Product.\u003c\/p\u003e \u003cp\u003eAppendix 5. Lattices.\u003c\/p\u003e \u003cp\u003eAppendix 6. Fast Matrix Multiplication.\u003c\/p\u003e \u003cp\u003eAppendix 7. Gershgorin's Theorem.\u003c\/p\u003e \u003cp\u003eAppendix 8. The Multiplicity of Eigenvalues.\u003c\/p\u003e \u003cp\u003eAppendix 9. The Fast Fourier Transform.\u003c\/p\u003e \u003cp\u003eAppendix 10. The Spectral Radius.\u003c\/p\u003e \u003cp\u003eAppendix 11. The Lorentz Group.\u003c\/p\u003e \u003cp\u003eAppendix 12. Compactness of the Unit Ball.\u003c\/p\u003e \u003cp\u003eAppendix 13. A Characterization of Commutators.\u003c\/p\u003e \u003cp\u003eAppendix 14. Liapunov's Theorem.\u003c\/p\u003e \u003cp\u003eAppendix 15. The Jordan Canonical Form.\u003c\/p\u003e \u003cp\u003eAppendix 16. Numerical Range.\u003c\/p\u003e \u003cp\u003eIndex.\u003c\/p\u003e \u003cp\u003e\u003ci\u003e\u003cb\u003eFunctional Analysis\u003c\/b\u003e\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003eForeword.\u003c\/p\u003e \u003cp\u003eLinear Spaces.\u003c\/p\u003e \u003cp\u003eLinear Maps.\u003c\/p\u003e \u003cp\u003eThe Hahn-Banach Theorem.\u003c\/p\u003e \u003cp\u003eApplications of the Hahn-Banach Theorem.\u003c\/p\u003e \u003cp\u003eNormed Linear Spaces.\u003c\/p\u003e \u003cp\u003eHilbert Space.\u003c\/p\u003e \u003cp\u003eApplications of Hilbert Space Results.\u003c\/p\u003e \u003cp\u003eDuals of Normed Linear Space.\u003c\/p\u003e \u003cp\u003eApplications of Duality.\u003c\/p\u003e \u003cp\u003eWeak Convergence.\u003c\/p\u003e \u003cp\u003eApplications of Weak Convergence.\u003c\/p\u003e \u003cp\u003eThe Weak and Weak* Topologies.\u003c\/p\u003e \u003cp\u003eLocally Convex Topologies and the Krein-Milman Theorem.\u003c\/p\u003e \u003cp\u003eExamples of Convex Sets and their Extreme Points.\u003c\/p\u003e \u003cp\u003eBounded Linear Maps.\u003c\/p\u003e \u003cp\u003eExamples of Bounded Linear Maps.\u003c\/p\u003e \u003cp\u003eBanach Algebras and their Elementary Spectral Theory.\u003c\/p\u003e \u003cp\u003eGelfand's Theory of Commutative Banach Algebras.\u003c\/p\u003e \u003cp\u003eApplications of Gelfand's Theory of Commutative Banach Algebras.\u003c\/p\u003e \u003cp\u003eExamples of Operators and their Spectra.\u003c\/p\u003e \u003cp\u003eCompact Maps.\u003c\/p\u003e \u003cp\u003eExamples of Compact Operators.\u003c\/p\u003e \u003cp\u003ePositive Compact Operators.\u003c\/p\u003e \u003cp\u003eFredholm's Theory of Integral Equations.\u003c\/p\u003e \u003cp\u003eInvariant Subspaces.\u003c\/p\u003e \u003cp\u003eHarmonic Analysis on a Halfline.\u003c\/p\u003e \u003cp\u003eIndex Theory.\u003c\/p\u003e \u003cp\u003eCompact Symmetric Operators in Hilbert Space.\u003c\/p\u003e \u003cp\u003eExamples of Compact Symmetric Operators.\u003c\/p\u003e \u003cp\u003eTrace Class and Trace Formula.\u003c\/p\u003e \u003cp\u003eSpectral Theory of Symmetric, Normal and Unitary Operators.\u003c\/p\u003e \u003cp\u003eSpectral Theory of Self-Adjoint Operators.\u003c\/p\u003e \u003cp\u003eExamples of Self-Adjoint Operators.\u003c\/p\u003e \u003cp\u003eSemigroups of Operators.\u003c\/p\u003e \u003cp\u003eGroups of Unitary Operators.\u003c\/p\u003e \u003cp\u003eExamples of Strongly Continuous Semigroups.\u003c\/p\u003e \u003cp\u003eScattering Theory.\u003c\/p\u003e \u003cp\u003eA Theorem of Beurling.\u003c\/p\u003e \u003cp\u003eAppendix A: The Riesz-Kakutani Representation Theorem.\u003c\/p\u003e \u003cp\u003eAppendix B: Theory of Distributions.\u003c\/p\u003e \u003cp\u003eAppendix C: Zorn's Lemma.\u003c\/p\u003e \u003cp\u003eAuthor Index.\u003c\/p\u003e \u003cp\u003eSubject Index.\u003c\/p\u003e  \u003cp\u003e\u003cstrong\u003ePeter D. Lax\u003c\/strong\u003e is a Series Advisor for the \u003cem\u003eWiley Interscience Series in Pure and Applied Mathematics\u003c\/em\u003e. He is a professor of mathematics at the Courant Institute, the director of the Mathematics and computing Laboratory, and was director of the Institute from 1971 to 1980.\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47989531082981,"sku":"NP9780470555545","price":227.95,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9780470555545.jpg?v=1761784483","url":"https:\/\/k12savings.com\/products\/linear-algebra-and-its-applications-2e-functional-analysis-set-isbn-9780470555545","provider":"K12savings","version":"1.0","type":"link"}