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On the Geographical Interpretation of Eigenvalues

P. R. Gould
Transactions of the Institute of British Geographers
No. 42 (Dec., 1967), pp. 53-86
DOI: 10.2307/621372
Stable URL: http://www.jstor.org/stable/621372
Page Count: 34
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On the Geographical Interpretation of Eigenvalues
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Abstract

This paper examines the possible uses of eigenvalues, the latent roots of square matrices, in enlarging understanding of the geographical features so effectively portrayed on maps. Since Laplace's studies of the perturbations of the planets, matrices have played an important role in other fields of study in reordering known facts to provide new insights. By transforming cartographical data into numbers, which are mathematically far more tractable, similar insights may be forthcoming in geography. After a consideration of the nature of eigenvalues and their associated eigenvectors, a wide variety of different applications is examined by reference to specific examples. These include analyses of terrain roughness on the New Jersey Coastal Plain, the Allegheny Plateau and the adjacent Ridge and Valley Province; connectivity matrices, as applied to the study of road networks in Uganda and Syria at different periods; the orientation of features as different as stream pebbles and transport networks in Tanzania and Sierra Leone; the diffusion of information; regional classification, by reference to church forms in Centre County, Pennsylvania; and principal components, in relation to the ranked preferences of university students in Ghana and Europe for different areas. Suggestions are offered for the further development of analyses of this kind, which may help to provide many more truly geographical explanations.

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