This book discusses structure theory of an operator, topics on inner product spaces, and trace and determinant functions of a linear operator. It addresses bilinear forms with a full treatment of symplectic spaces and orthogonal spaces, as well as explains construction of tensor, symmetric, and exterior algebras. Featuring several new exercises, the second edition adds coverage of sesquilinear forms, linear groups, matrices, normed vector spaces, orthogonal spaces over perfect fields of characteristic two, and Clifford algebras. A solutions manual is available upon qualifying course adoption.

Vector Spaces. Linear Transformations. Polynomials. Theory of a Single Linear Operator. Normed and Inner Product Spaces. Linear Operators on Inner Product Spaces. Trace and Determinant of a Linear Operator. Bilinear Forms. Sesquilinear Forms and Unitary Geometry. Tensor Products. Linear Groups and Groups of Isometries. Additional Topics in Linear Algebra. Applications of Linear Algebra. Appendices.

Bruce Cooperstein is a professor of mathematics at the University of California, Santa Cruz, USA. He was a visiting scholar at the Carnegie Foundation for the Advancement of Teaching (spring 2007) and a recipient of the Kellogg National Fellowship (1982-1985) and the Pew National Fellowship for Carnegie Scholars (1999-2000). Dr. Cooperstein has authored numerous papers in refereed mathematics journals.