Singular random matrix decompositions: distributions.

Assuming that Y has a singular matrix variate elliptically contoured distribution with respect to the Hausdorff measure, the distributions of several matrices associated to QR, modified QR, SV and Polar decompositions of matrix Y are determined, for central and non-central, non-singular and singular cases, as well as their relationship to the Wishart and Pseudo-Wishart generalized singular and non-singular distributions. We present a particular example for the Karhunen-Lòeve decomposition. Some of these results are also applied to two particular subfamilies of elliptical distributions, the singular matrix variate normal distribution and the singular matrix variate symmetric Pearson type VII distribution

Singular random matrix decompositions: Jacobians.

For a singular random matrix Y, we find the Jacobians associated with the following decompositions; QR, Polar, Singular Value (SVD), L'U, L'DM and modified QR (QDR). Similarly, we find the Jacobinas of the following decompositions: Spectral, Cholesky's, L'DL and symmetric non-negative definite square root, of the cross-product matrix S = Y'Y

Curvature function and coarse graining

A classic theorem in the theory of connections on principal fiber bundles states that the evaluation of all holonomy functions gives enough information to characterize the bundle structure (among those sharing the same structure group and base manifold) and the connection up to a bundle equivalence map. This result and other important properties of holonomy functions has encouraged their use as the primary ingredient for the construction of families of quantum gauge theories. However, in these applications often the set of holonomy functions used is a discrete proper subset of the set of holonomy functions needed for the characterization theorem to hold. We show that the evaluation of a discrete set of holonomy functions does not characterize the bundle and does not constrain the connection modulo gauge appropriately. We exhibit a discrete set of functions of the connection and prove that in the abelian case their evaluation characterizes the bundle structure (up to equivalence), and constrains the connection modulo gauge up to "local details" ignored when working at a given scale. The main ingredient is the Lie algebra valued curvature function $F_S (A)$ defined below. It covers the holonomy function in the sense that $\exp{F_S (A)} = {\rm Hol}(l= \partial S, A)$.Comment: 34 page

Performance Measurement Systems, Competitive Priorities, and Advanced Manufacturing Technologies: Some Evidence from the Aeronautical Sector

Purpose – When acquiring advanced manufacturing technologies (AMT), the greatest caution should be taken regarding the performance measurement system to be used: the decision regarding new investments should not be conditioned by the excessive use of financial indicators to the detriment of the strategic objectives that motivated the investments. It is intended to analyze the aeronautical sector, for which the purchase of AMT is qualifying criteria, with two intentions: first, to identify the performance measurement systems that are used, and second, to test their correspondence with the objectives that motivated the investments. Design/methodology/approach – A survey of the 20 plants in the population was conducted via a postal questionnaire plus a structured interview. The unit of analysis has been maintained through the triangulation of data sources. Findings – The findings suggest that both financial and non-financial indicators are used, with the latter gaining predominance over the former on some occasions, even though there is no clear correspondence between strategy and the measurement of performance. In the light of the findings, the question of what inspires a company’s performance measurement system is still open, especially in those cases where there is no explicit strategy. With regard to practical implications, what seems to be indispensable is an improvement in the determination of the critical variables that should be used to measure performance. Research limitations/implications – Being valuable for academics and practitioners, this contribution relies, rather, on the possibility of a logical extrapolation to circumstances where the findings might apply, and researchers can judge whether the particular findings would be valid. Originality/value – Provides new evidence on the adaptation of the make-up and combination of the type of performance measures currently used by plants in the aeronautical industry, one of the sectors in which technological innovation is of the utmost importance.Publicad

SINGULAR RANDOM MATRIX DECOMPOSITIONS: DISTRIBUTIONS.

Assuming that Y has a singular matrix variate elliptically contoured distribution with respect to the Hausdorff measure, the distributions of several matrices associated to QR, modified QR, SV and Polar decompositions of matrix Y are determined, for central and non-central, non-singular and singular cases, as well as their relationship to the Wishart and Pseudo-Wishart generalized singular and non-singular distributions. We present a particular example for the Karhunen-Lòeve decomposition. Some of these results are also applied to two particular subfamilies of elliptical distributions, the singular matrix variate normal distribution and the singular matrix variate symmetric Pearson type VII distribution.