Abstract
For a given vector A := (a0,a1,...,an−1) in ℝn, simple necessary and sufficient conditions on a0,a1,...,an−1 are established for the determinant of the circulant matrix of A to be positive, or negative, or zero. There is a striking difference between the conditions for n odd and the conditions for n even. The determinant of the skew-circulant matrix of A is similarly discussed.
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References
Richard Bellman, Introduction to matrix analysis, 2nd edition, McGraw-Hill Book Company, New York, 1970.
Gerhard Kowalewski, Einführung in die Determinantentheorie, Walter de Gruyter, Berlin, 1942.
Marvin Marcus and Henryk Mine, A survey of matrix theory and matrix inequalities, Allyn and Bacon, Boston, 1964.
Thomas Muir and William H. Metzler, A treatise on the theory of determinants, Dover Publications, New York, 1960.
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© 1978 Springer Basel AG
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Beckenbach, E.F., Bellman, R. (1978). On the Positivity of Circulant and Skew-Circulant Determinants. In: Beckenbach, E.F. (eds) General Inequalities 1 / Allgemeine Ungleichungen 1. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale d’Analyse Numérique, vol 41. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5563-1_6
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DOI: https://doi.org/10.1007/978-3-0348-5563-1_6
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-5565-5
Online ISBN: 978-3-0348-5563-1
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