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NOTE ON ‘THE JACOBIANS OF CERTAIN MATRIX TRANSFORMATIONS USEFUL IN MULTIVARIATE ANALYSIS’

1953; Oxford University Press; Volume: 40; Issue: 1-2 Linguagem: Inglês

10.1093/biomet/40.1-2.43

1464-3510

Ingram Olkin,

Matrix Theory and Algorithms

General techniques for the evaluation of the Jacobian of a matrix transformation were outlined by Deemer & Olkin (1951). In particular, (a) the Jacobian of a non-linear transformation is equal to the Jacobian of the linear transformation in the differentials, (b) by the introduction of suitable variables, the Jacobian is equal to a product of Jacobians which are easily calculated. This note is concerned with a number of transformations not considered in the earlier paper. Certain of the transformations considered will be recognized as extensions of those given previously, while others are quite different. The notation and results of the first paper are assumed. All matrices in this note are square of order p.