Abstract
Eigenvalues and eigenvectors are defined. The Spectral Theorem for symmetric matrices is proved. Positive definite matrices are introduced. Idempotent matrices are defined and it is shown that for such matrices the rank equals the trace. Schur complement is defined and its application to proving characterizations of positive definite matrices is shown.
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© 2012 Springer-Verlag London Limited
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Bapat, R.B. (2012). Eigenvalues and Positive Definite Matrices. In: Linear Algebra and Linear Models. Universitext. Springer, London. https://doi.org/10.1007/978-1-4471-2739-0_3
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DOI: https://doi.org/10.1007/978-1-4471-2739-0_3
Publisher Name: Springer, London
Print ISBN: 978-1-4471-2738-3
Online ISBN: 978-1-4471-2739-0
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