Resumen

Este artículo presenia una aproximación elemental al estudio de la matriz de proyeccian de poblaci'on, el reverso (o inversa) matriz de proyección, el proceso de desarrollo de la poblacian generado por la matriz de proyección, el “a priori” proceso de desarrollo de población asociado con la matriz de proyección inversa, la distribución de edades eetoble que pertenece a la matriz de proyección, la ecuación característica de la matriz de proyección y las raices laienies de la ecuación característica.

Nosotros introducimos algunos nuevos indices que miden el “valor reproductivo eventual” de los individuos en los varios intervalos de edades de una población, y mostramos porque los índices presentados aquí son preferibles a los indices de la misma naturaleza presentados anteriormente por R. A. Fisher y P. H. Leslie.

Para poder seguir la mayor parte de la presenie exposición, el lector precisa iener solamenie nociones elemeniales de algunos de los terminosusados en algebra de matrics. Esta aproximación elemental va a llevarnos a la introducción de algunas nuevas fórmulas las cuoles simplijican a la vez la comprensión y el cálculo de varias cantidades que son relevantes a la demografiá y a la teoría matemática del desarrollo de la población.

Summary

This article presents an elementary approach to the study of the population projection-matrix, the reverse (or inverse) projection-matrix, the process of population growth generated by the projection-matrix, the “prior” process of population growth associated with the reverse projection-matrix, the stable age-distribution that pertains to the projection-matrix, the characteristic equation of the projection-matrix, and the latent roots of the characteristic equation. We also introduce some new indices that measure the “eventual reproductive value” of the individuals in the various ageintervals in a population, and we show why the indices presented here. are preferable to a related index presented earlier by R. A. Fisher and P. H. Leslie.

In order to follow the major part of the present exposition, the reader will need only a beginner's understanding of a few of the terms used in matrix algebra. This elementary approach will lead to the introduction of some new formulas that will simplify both the understanding and the calculation of various quantities that are relevant to demography and to the mathematical theory of population growth.

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