This text is designed to teach the concepts and techniques of basic linear algebra as a rigorous mathematical subject. Besides computational proficiency, there is an emphasis on understanding definitions and theorems, as well as reading, understanding and creating proofs. A strictly logical organization, complete and exceedingly detailed proofs of every theorem, advice on techniques for reading and writing proofs, and a selection of challenging theoretical exercises will slowly provide the novice with the tools and confidence to be able to study other mathematical topics in a rigorous fashion.

Contents

• Systems of Linear Equations
• Vectors
• Matrices
• Vector Spaces
• Determinants
• Eigenvalues
• Linear Transformations
• Representations
• Preliminaries
• Reference

Summary on tutorial A First Course in Linear Algebra

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