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- catalog abstract "This text for a second course in linear algebra is aimed at math majors and graduate students. The novel approach taken here banishes determinants to the end of the book and focuses on the central goal of linear algebra: understanding the structure of linear operators on vector spaces. The author has taken unusual care to motivate concepts and to simplify proofs. For example, the book presents - without having defined determinants - a clean proof that every linear operator on a finite-dimensional complex vector space (or an odd-dimensional real vector space) has an eigenvalue. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra. No prerequisites are assumed other than the usual demand for suitable mathematical maturity. Thus the text starts by discussing vector spaces, linear independence, span, basis, and dimension. Students are introduced to inner-product spaces in the first half of the book and shortly thereafter to the finite-dimensional spectral theorem. This second edition includes a new section on orthogonal projections and minimization problems. The sections on self-adjoint operators, normal operators, and the spectral theorem have been rewritten. New examples and new exercises have been added, several proofs have been simplified, and hundreds of minor improvements have been made throughout the text.".
- catalog contributor b11430150.
- catalog created "c1997.".
- catalog date "1997".
- catalog date "c1997.".
- catalog dateCopyrighted "c1997.".
- catalog description "This text for a second course in linear algebra is aimed at math majors and graduate students. The novel approach taken here banishes determinants to the end of the book and focuses on the central goal of linear algebra: understanding the structure of linear operators on vector spaces. The author has taken unusual care to motivate concepts and to simplify proofs. For example, the book presents - without having defined determinants - a clean proof that every linear operator on a finite-dimensional complex vector space (or an odd-dimensional real vector space) has an eigenvalue. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra. No prerequisites are assumed other than the usual demand for suitable mathematical maturity. Thus the text starts by discussing vector spaces, linear independence, span, basis, and dimension. Students are introduced to inner-product spaces in the first half of the book and shortly thereafter to the finite-dimensional spectral theorem. This second edition includes a new section on orthogonal projections and minimization problems. The sections on self-adjoint operators, normal operators, and the spectral theorem have been rewritten. New examples and new exercises have been added, several proofs have been simplified, and hundreds of minor improvements have been made throughout the text.".
- catalog description "Vector Spaces -- Finite-Dimensional Vector Spaces -- Linear Maps -- Polynomials -- Eigenvalues and Eigenvectors -- Inner-Product Spaces -- Operators on Inner-Product Spaces -- Operators on Complex Vector Spaces -- Operators on Real Vector Spaces -- Trace and Determinant -- Symbol Index -- Index.".
- catalog extent "xv, 251 p. :".
- catalog identifier "0387982582 (pbk. : alk. paper)".
- catalog identifier "0387982590 (alk. paper)".
- catalog isPartOf "Undergraduate texts in mathematics".
- catalog issued "1997".
- catalog issued "c1997.".
- catalog language "eng".
- catalog publisher "New York : Springer,".
- catalog subject "512/.5 21".
- catalog subject "Algebras, Linear.".
- catalog subject "Mathematics.".
- catalog subject "Matrix theory.".
- catalog subject "QA184 .A96 1997".
- catalog tableOfContents "Vector Spaces -- Finite-Dimensional Vector Spaces -- Linear Maps -- Polynomials -- Eigenvalues and Eigenvectors -- Inner-Product Spaces -- Operators on Inner-Product Spaces -- Operators on Complex Vector Spaces -- Operators on Real Vector Spaces -- Trace and Determinant -- Symbol Index -- Index.".
- catalog title "Linear algebra done right / Sheldon Axler.".
- catalog type "text".