Abstract
In this chapter, we discuss some of the elementary properties of permutation and reflection matrices. We define a class of reflection matrices related to the Samuelson—Wise conditions for the stability of a linear difference equation and we discuss a class of permutation matrices associated with functions defining chaotic and sub-chaotic pseudo-random processes.
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References
Downham, D.Y., and Roberts, F.D.K.(1967), Multiplicative Congruential Pseudo-Random Number Generators, Computer Journal 2, 74–77.
Farebrother, R.W., (1973), Simplified Samuelson Conditions for Cubic and Quartic Equations, The Manchester School, 41, 396–400. Reprinted in J.C. Wood and R.N. Woods (1988), Vol. 2, 197–203.
Farebrother, R.W., (1974a), Simplified Samuelson Conditions for Quintic Equations, The Manchester School, 42, 279–282. Reprinted in J.C. Wood and R.N. Woods (1988), Vol. 2, 276–279.
Farebrother, R.W., (1974b), Recursive Relations for the Samuelson Transformation Coefficients, International Economic Review, 15: 805–807. Reprinted in J.C. Wood and R.N. Woods (1988), Vol. 2, 280–282.
Farebrother, R.W.(1987) Independent Conditions for the Stability of a Dynamic Linear Model, The Manchester School, 55, 305–309.
Farebrother, R.W., (1988), Linear Least Squares Computations, Marcel Dekker Inc., New York.
Farebrother, R.W., (1992), A Note on the Schur and Samuelson Conditions, The Manchester School, 60, 79–81.
Farebrother, R.W., (1996), The Role of Chaotic Processes in Econometric Models, Journal of Statistical Planning and Inference, 49, 163–176.
Hedayat, A., and W. Wallis, (1978), Hadamard Matrices, Annals of Statistics, 6, 1184–1234.
Pollock, D.S.G., (1996), Stability Conditions for Linear Stochastic models: A Survey, Paper presented at the Fifth International Workshop on Matrix Methods for Statistics, Shrewsbury.
Samuelson, P.A., (1941), Conditions that the Roots of a Polynomial be Less than Unity in Absolute Value, Annals of Mathematical Statistics, 12, 360–364.
Van der Waerden, B.L., (1983), Geometry and Algebra in Ancient Civilizations, Springer-Verlag, Berlin.
Wise, J., (1956), Stationarity Conditions for Stochastic Processes of the Autoregressive and Moving Average Type, Biometrika, 43: 215–219.
Wood, J.C., and R.N. Woods, (1988), Paul A. Samuelson: A Critical Assessment, Routledge, London.
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Farebrother, R.W. (2000). Notes on the Elementary Properties of Permutation and Reflection Matrices. In: Heijmans, R.D.H., Pollock, D.S.G., Satorra, A. (eds) Innovations in Multivariate Statistical Analysis. Advanced Studies in Theoretical and Applied Econometrics, vol 36. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-4603-0_13
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DOI: https://doi.org/10.1007/978-1-4615-4603-0_13
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-7080-2
Online ISBN: 978-1-4615-4603-0
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