Finkbeiner D. Introduction to Matrices and Linear Transform 1960

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The obvious purpose of this book is to present a lucid and unified introduction to linear algebra at a level which can be understood by undergraduates who possess reasonable mathematical aptitude, and thus to lay a solid foundation from which each student can apply these notions and techniques to the field of his interest. A more subtle but equally serious objective is to prepare the student for advanced scientific work by developing his powers of abstract reasoning.
Abstract Systems
Vector Spaces
Linear Transformations
Matrices
Linear Equations and Determinants
Equivalence Relations on Matrices
Characteristics of a Matrix
A Canonical Form for Linear Transformations
Metric Concepts
Functions of Matrices
Appendix
Algebraic Concepts
Combinatorial Equivalence
References
Suggestions and Answers for Selected Exercises
Index