# The Discrete Time Matrix Model

Chapter

## Abstract

The discrete time recurrence model and the continuous time model which were discussed in Chapters Three and Four focused on the births that occurred at a particular time and their relationship to the births that occurred prior to this time. In each case the age distribution of the population was discussed almost as an adjunct to the model and not as an integral part of it. Perhaps this was unfortunate since it was the asymptotic age distribution of the model that gave meaning to the concept of a ‘stable’ population.

## Keywords

Transition Matrix Stable Theory Projection Matrix Transition Matrice Principal Eigenvalue
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## Notes for Chapter Five

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- [3]Leslie, P.H. (1945), On the use of matrices in certain population mathematics. Biometrika, vol. 33, pp. 183–212.CrossRefMATHMathSciNetGoogle Scholar
- [4]Ibid., p. 187.Google Scholar
- [5]Ibid., p. 187.Google Scholar
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- [9]Gantmacher, op. cit., p. 64 ff.Google Scholar
- [10]Ibid., p.Google Scholar
- [11]Meyer, W. (1982), Asymptotic birth trajectories in the discrete form of stable population theory. Theoretical Population Biology, vol. 21, no. 2, pp. 167–170.CrossRefMATHMathSciNetGoogle Scholar
- [12]The development of this section is primarily due to the invention of the author.Google Scholar
- [13]Moore, John T. (1968), Elements of linear algebra and matrix theory, p. 327 ff.Google Scholar
- [14]Noble, Ben (1969), Applied linear algebra, p. 361 ff.MATHGoogle Scholar
- [15]Pollard, J.H. (1973), Mathematical models for the growth of human populations, pp. 44–45.MATHGoogle Scholar
- [16]Noble, Ben, op. cit., pp. 363–366.Google Scholar
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