Linear algebra done right - Axler, Sheldon Jay (New York, NY Springer-Verlag New York, Inc., 1997)
"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."--Book jacket.
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.
Includes indexes.
Keywords: Algebras, Linear