Abstract
The basic eigenvalue analysis of real symmetric matrices was discussed in Chapter 1. The eigenvalue properties described there are shared by all positive-definite (or semi-definite) matrices. This chapter, which may be missed on a first reading, provides proofs of some of the results which were used in Chapter 1. Foremost among these are Theorem 5.3.1, that a real symmetric matrix has N real eigenvectors which are orthonormal, and thus span the vector space; and Theorem 5.3.7 which provides necessary and sufficient conditions for the matrix A to be positive definite.
There are then two kinds of intellect: the one able to penetrate acutely and deeply into the conclusions of given premises, and this is the precise intellect; the other able to comprehend a great number of premises without confusing them, and this is the mathematical intellect.
Pascal’s Pensées
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© 1986 Martinus Nijhoff Publishers, Dordrecht
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Gladwell, G.M.L. (1986). Further Properties of Matrices. In: Inverse problems in vibration. Mechanics: Dynamical Systems, vol 9. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-1178-0_5
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DOI: https://doi.org/10.1007/978-94-015-1178-0_5
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-015-1180-3
Online ISBN: 978-94-015-1178-0
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