Positive Definiteness, Matrix Factorization, and an Imperfect Analogy

David F. Delchamps
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David F. Delchamps: Cornell University, School of Electrical Engineering

Chapter 12 in State Space and Input-Output Linear Systems, 1998, pp 162-175 from Springer

Abstract: Abstract The results of this section are purely algebraic, but they will prove to be of great significance in §§13–15 when we discuss linear matrix equations, reachability, and observability, and again in Part in when realization theory for time-invariant input-output systems is treated. The “imperfect analogy” to which the section title alludes is a rough parallel which we draw between the family of real (n × n) matrices and the family of complex numbers; the reader may judge independently whether this correspondence is a useful or interesting one.

Date: 1998
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DOI: 10.1007/978-1-4612-3816-4_13

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