A generalization of Kristof's theorem on the trace of certain matrix products

Kristof has derived a theorem on the maximum and minimum of the trace of matrix products of the form \(X_1 \hat \Gamma _1 X_2 \hat \Gamma _2 \cdots X_n \hat \Gamma _n\) where the matrices \(\hat \Gamma _i\) are diagonal and fixed and theX _i vary unrestrictedly and independently over the set of orthonormal matrices. The theorem is a useful tool in deriving maxima and minima of matrix trace functions subject to orthogonality constraints. The present paper contains a generalization of Kristof's theorem to the case where theX _i are merely required to be submatrices of orthonormal matrices and to have a specified maximum rank. The generalized theorem contains the Schwarz inequality as a special case. Various examples from the psychometric literature, illustrating the practical use of the generalized theorem, are discussed.     

Dilthey''s narrative model of human development: Necessary reconsiderations after the philosophical hermeneutics of Heidegger and Gadamer

Paper delivered at theEighth International Human Science Research Conference at Aarhus University (Denmark), 18–22 August 1989.     

Some clarifications of the CANDECOMP algorithm applied to INDSCAL

Carroll and Chang have claimed that CANDECOMP applied to symmetric matrices yields equivalent coordinate matrices, as needed for INDSCAL. Although this claim has appeared to be valid for all practical purposes, it has gone without a rigorous mathematical footing. The purpose of the present paper is to clarify CANDECOMP in this respect. It is shown that equivalent coordinate matrices are not granted at global minima when the symmetric matrices are not Gramian, or when these matrices are Gramian but the solution not globally optimal.Part of this research has been supported by The Netherlands Organization for Scientific Research (NWO), PSYCHON-grant (560-267-011).     

Does awareness of speech as a sequence of phones arise spontaneously?

It was found that illiterate adults could neither delete nor add a phone at the beginning of a non-word; but these tasks were rather easily performed by people with similar environment and childhood experiences, who learned to read rudimentarily as adults. Awareness of speech as a sequence of phones is thus not attained spontaneously in the course of general cognitive growth, but demands some specific training, which, for most persons, is probably provided by learning to read in the alphabetic system.     

Perception,belief, and the structure of physical objects and consciousness

Conclusion We have now provided an overall simple theoretical account of the structure of perceptual experience proto-philosophically examined in Part I. The next task is to find the proper logical machinery to formulatte those accounts rigorously.This essay is an abridgment of a monograph written while the author enjoyed both a 1975–76 sabbatical leave from Indiana University and a concurrent grant from the National Endowment for the Humanities for doing research in metaphysics.     

Associating Ethos with Objects: Reasoning from Character of Public Figures to Actions in the World

Argumentation - Ethotic arguments, such as arguments from expert opinion and ad hominem arguments, play an important role in communication practice. In this paper, we argue that there is another...