Scalar Products

I. Borg and J. Lingoes
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I. Borg: Justus-Liebig-Universität, Department of Psychology
J. Lingoes: University of Michigan, Computing Center

Chapter 16 in Multidimensional Similarity Structure Analysis, 1987, pp 250-269 from Springer

Abstract: Abstract We consider the notion of a scalar product, a function closely associated with distance, involving vectors. We then ask whether there are empirical similarity judgments which can be interpreted as scalar products. This leads to questions like “How much of A is contained in B?”. Scores from experiments asking this kind of question are used in different ways to build scalar products. Since distance judgments can be collected directly, but scalar products are easier to handle numerically, we ask whether distances can be converted into scalar products.

Keywords: scalar product; vector configuration; contained-in judgment; ratio judgment; rotation of axes; simple structure; reconstructed scalar product; varimax; extraction of principal components; scalar products and distances; communality and totality of subjective stimulus intensities; stimulus quality and intensity (search for similar items in EconPapers)
Date: 1987
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DOI: 10.1007/978-1-4612-4768-5_16

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