Blyth T. Algebra through Practice Vol 4. Linear Algebra 1985

Textbook in PDF format

A collection of problems in algebra with solutions.
Problem-solving is an art central to understanding and ability in mathematics. With this series of books, the authors have provided a selection of worked examples, problems with complete solutions and test papers designed to be used with or instead of standard textbooks on algebra. For the convenience of the reader, a key explaining how the present books may be used in conjunction with some of the major textbooks is included. Each volume is divided into sections that begin with some notes on notation and prerequisites. The majority of the material is aimed at the students of average ability but some sections contain more challenging problems. By working through the books, the student will gain a deeper understanding of the fundamental concepts.
Background reference material
Direct sums and Jordan forms
Duality and normal transformations
Solutions
Test papers