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Matrix Calculus

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Measurement, Mathematics and New Quantification Theory

Part of the book series: Behaviormetrics: Quantitative Approaches to Human Behavior ((BQAHB,volume 16))

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Abstract

When we deal with many variables, the designation of a variable by a subscript becomes cumbersome. Once we introduce the matrix notation, the expression of formulas with many variables can not only be vastly simplified, but it also leads to new mathematics of many variables in a unified way.

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References

  • Bock, R. D. (1975). Multivariate statistical methods in behavioral research. McGraw-Hill.

    Google Scholar 

  • Browne, E. T. (1958). Introduction to the theory of determinants and matrices. The University of North Carolina Press.

    Google Scholar 

  • Curtis, C. W. (1963). Linear Algebra: An introductory approach. Allyn and Bacon.

    Google Scholar 

  • Feeman, G. F., & Grabois, N. R. (1970). Linear Algebra and multivariable calculus. McGraw-Hill.

    Google Scholar 

  • Graybill, F. A. (1961). An introduction to linear statistical models. McGraw-Hill.

    Google Scholar 

  • Graybill, F. A. (1969). Introduction to matrices with applications in statistics. Wadsworth Publishing Company.

    Google Scholar 

  • Graybill, F. A. (1976). Theory and application of linear model. Wadsworth Publishing Company.

    Google Scholar 

  • Horst, P. (1963). Matrix Algebra for social scientists. Rinehart and Winston: Holt.

    Google Scholar 

  • Nishisato, S. (1984). Forced classification: A simple application of a quantification technique. Psychometrika, 49, 25–36.

    Google Scholar 

  • Nishisato, S., & Baba, Y. (1999). On contingency, projection and forced classification of dual scaling. Behaviormetrika, 26, 207–219.

    Google Scholar 

  • Nishisato, S. (1980). Analysis of Categorical Data: Dual Scaling and Its Applications. Toronto: The University of Toronto Press

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  • Nishisato, S., & Lawrence, D. R. (1989). Dual scaling of multiway data matrices: Several variants. In R. Coppi & S. Bolasco (Eds.), Multiway data analysis (pp. 317–326). Elsevier Science Publishers.

    Google Scholar 

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Authors and Affiliations

  1. Professor Emeritus, University of Toronto, Toronto, ON, Canada

    Shizuhiko Nishisato

Authors
  1. Shizuhiko Nishisato
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Correspondence to Shizuhiko Nishisato .

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© 2023 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

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Nishisato, S. (2023). Matrix Calculus. In: Measurement, Mathematics and New Quantification Theory. Behaviormetrics: Quantitative Approaches to Human Behavior, vol 16. Springer, Singapore. https://doi.org/10.1007/978-981-99-2295-6_4

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