Partitioned Kronecker products of matrices and applications. (English) Zbl 0684.62044
Summary: Some generalized commutation matrices are defined and used to establish relationships between \(\pi\)-products and Kronecker products. These are applied to obtain expectations of \(\pi\)-products of random vectors and matrices.
MSC:
62H99 | Multivariate analysis |
15A69 | Multilinear algebra, tensor calculus |
15B52 | Random matrices (algebraic aspects) |
Keywords:
pi-products; balanced; partitioning; expectations; multivariate normal distribution; generalized commutation matrices; Kronecker productsReferences:
[1] | Browne, The maximum likelihood in interbatrtery factor analysis, British J. Math. Statist. Psych. 32 pp 75– (1979) · Zbl 0404.62079 · doi:10.1111/j.2044-8317.1979.tb00753.x |
[2] | MacRae, Matrix derivatives with an application to an adaptive linear decision problem, Ann. Statist. 2 pp 337– (1974) · Zbl 0285.26013 |
[3] | Magnus, Linear Structures (1988) |
[4] | Magnus, The commutation matrix: Some properties and applications, Ann. Statist. 7 pp 381– (1979) · Zbl 0414.62040 |
[5] | Neudecker, Some results on commutation matrices with statistical applications, Canad. J. Statist. 11 pp 221– (1983) · Zbl 0538.15011 |
[6] | Singh, R. P. (1972). Some generalizations in matrix differentiation with applications in multivariate analysis. Ph. D. Dissertation, University of Windsor. |
[7] | Tracy, Multivariate maxima and minima with matrix derivatives, J. Amer. Statist. Assoc. 64 pp 1576– (1969) |
[8] | Tracy, On generalized least squares estimation in inter-battery factor analysis, Pakistan J. Statist. 1 pp 79– (1985) · Zbl 0615.62070 |
[9] | Tracy, A new matrix product and its applications in partitioned matrix differentiation, Statist. Neerland. 26 pp 143– (1972) · Zbl 0267.15009 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.