### On The Relationship Between The Matrix Operators of vech* and vecp*

#### Abstract

This article discusses two new matrix operators constructed differently from and by taking a square matrix's main diagonal and supra-diagonal entries. We call these two operators the and . We explicitly construct a matrix that transforms to , where is an matrix for . We also derive various properties from the matrix.

Keywords— permutation matrix; vecp*; vech*; vec operator

#### Keywords

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PDF#### References

H. V. Henderson and S. R. Searle, "Vec and vech operators for matrices, with some uses in Jacobians and multivariate statistics," The Canadian Journal of Statistics, vol. 7, no. 1, pp. 65-81, 1979.

K. G. Jinadasa, "Applications of the matrix operators vech and vec," Linear Algebra and Its Applications, vol. 101, pp. 73-79, 1988.

T. H. Szatrowski, "Asymptotic nonnull distributions for likelihood ratio statistics in the multivariate normal patterned mean and covariance matrix testing problem," The Annals of Statistics, vol. 7, no. 4, pp. 823-837, 1979.

Y. Hardy and W. Steeb, "Vec-operator, Kronecker product and entanglement," International Journal of Algebra and Computation, vol. 20, no. 1, pp. 71-76, 2010.

H. Zhang and F. Ding, "On the Kronecker products and their applications," Journal of Applied Mathematics, pp. 1-8, 2013.

R. H. Koning, H. Neudecker and T. Wansbeek, "Block Kronecker Products and the vecb Operator," Linear Algebra and Its Applications, vol. 149, pp. 165-184, 1991.

I. Ojeda, "Kronecker square roots and the block vec matrix," The American Mathematical Monthly, vol. 122, no. 1, pp. 60-64, 2015.

J. R. Schott, Matrix Analysis for Statistics, 3rd ed., New Jersey: John Wiley and Sons, 2017.

D. Nagakura, "On the matrix operator vecp," Available at SSRN: https://ssrn.com/abstract=2929422 or http://dx.doi.org/10.2139/ssrn.2929422, pp. 1-12, 2017.

D. Nagakura, "On the relationship between the matrix operator, vech and vecd," Communication in Statistics-Theory and Method, vol. 47, no. 13, pp. 3252-3268, 2017.

M. K. Abadir and J. R. Magnus, Matrix Algebra, USA: Cambridge University Press, 2005.

J. A. Gallian, Contemporary Abstract Algebra, 7 ed., Belmon, CA: Brooks/Cole, Cengage Learning, 2010.

R. Piziak and P. L. Odell, Matrix Theory: From Generalized Inverses to Jordan Form, New York: Chapmann & Hall/CRC, 2007.

H. Anton and C. Rorres, Elementary Linear Algebra: Application Version, 5th ed., New Jersey: Wiley, 2004.

DOI: http://dx.doi.org/10.52155/ijpsat.v38.1.5192

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