Using Leslie Matrices as the Application of Eigenvalues and Eigenvectors in a First Course in Linear Algebra

• Michael Monagan
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 1125)

Abstract

Leslie matrices may be used to model the age distribution of a population as well as population growth. The dominant eigenvalue tells us the long term population growth and the corresponding eigenvector tells us the long term age distribution. Because the model is so simple, and it does not require any knowledge of physics or chemistry or biology, it’s ideal for presenting in a first course on Linear Algebra as the main application of eigenvalues and eigenvectors.

In this paper we present the Leslie age distribution model and provide accompanying exercises suitable for students. We use Maple for both numerical calculations and symbolic calculations. We include some data for real populations that instructors may use for classroom presentation or for assignments.

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