Aimed at first year students, working from concrete examples towards abstract theorems, via tutorial-type exercises, this text explains the algebra of matrices with applications to analytic geometry, systems of linear equations, difference equations and complex numbers. It assumes very little prior knowledge. Features include treating linear equations via Hermite normal forms and a description of the connection between linear mappings and matrices.
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Preface.- Foreward.- The Algebra of Matrices.- Some Applications of Matrices.- Systems of Linear Equations.- Invertible Matrices.- Vector Spaces.- Linear Mappings.- The Matrix Connection.- Determinants.- Eigenvalues and Eigenvectors.- The Minimal Polynomial.- Solutions to the Exercises.- Index.
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