Abstract
We obtain the spectral decomposition of four linear mappings. The first, κ, is a mapping of the linear hull of all centered inner-product matrices onto the linear hull of all the induced squared-distance matrices. It is based on the natural generalization of the cosine law of elementary Euclidean geometry. The other three mappings studied are κ −1, the adjoint κ ∗, and (κ ∗) −1. Extensions and applications, particularly to multidimensional scaling, are discussed in some detail.
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