## Linear algebra done right

Sheldon Axler

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.

「Nielsen BookData」より

This text for a second course in linear algebra, aimed at math majors and graduates, adopts a novel approach by banishing determinants to the end of the book and focusing on 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 has an eigenvalue. The book starts by discussing vector spaces, linear independence, span, basics, 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. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra. This second edition features new chapters on diagonal matrices, on linear functionals and adjoints, and on the spectral theorem; some sections, such as those on self-adjoint and normal operators, have been entirely rewritten; and hundreds of minor improvements have been made throughout the text.

「Nielsen BookData」より

[目次]

• 1: Vector Spaces 2: Finite-Dimensional Vector Spaces 3: Linear Maps 4: Polynomials 5: Eigenvalues and Eigenvectors 6: Inner-Product Spaces 7: Operators on Inner-Product Spaces 8: Operators on Complex Vector Spaces 9: Operators on Real Vector Spaces 10: Trace and Determinant

「Nielsen BookData」より

[目次]

• 1: Vector Spaces 2: Finite-Dimensional Vector Spaces 3: Linear Maps 4: Polynomials 5: Eigenvalues and Eigenvectors 6: Inner-Product Spaces 7: Operators on Inner-Product Spaces 8: Operators on Complex Vector Spaces 9: Operators on Real Vector Spaces 10: Trace and Determinant

「Nielsen BookData」より

書名 Linear algebra done right Axler, Sheldon Jay Axler Sheldon Undergraduate texts in mathematics Springer c1997 2nd ed xv, 251 p. 25 cm 0387982582 0387982590 BA33116321 ※クリックでCiNii Booksを表示 英語 アメリカ合衆国
この本を：