Abstract
Linear algebra is an essential tool in many branches of mathematics and has wide applications. A large part of the subject consists of the study of homomorphisms of (finitely generated) free modules (in particular, linear transformations of finite dimensional vector spaces). There is a crucial relationship between such homomorphisms and matrices (Section 1). The investigation of the connection between two matrices that represent the same homomorphism (relative to different bases) leads to the concepts of equivalence and similarity of matrices (Sections 2 and 4). Certain important invariants of matrices under similarity are considered in Section 5. Determinants of matrices (Section 3) are quite useful at several points in the discussion.
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© 1974 Springer-Verlag New York, Inc.
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Hungerford, T.W. (1974). Linear Algebra. In: Algebra. Graduate Texts in Mathematics, vol 73. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-6101-8_8
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DOI: https://doi.org/10.1007/978-1-4612-6101-8_8
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-6103-2
Online ISBN: 978-1-4612-6101-8
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