On physical units in multivariate analysis
(2002) Abstract
 comparatively stringent mathematical frame has been developed, where the behaviour of physical dimensions (like ``length'', ``mass'', and
``time'') and physical units (like 1 m [1 metre], 1 kg [1 kilogramme], and 1 s [1 second]) is modelled. Easytoapply conditions for additivity and multiplicativity of physcial matrices are presented. Precise meanings of physically dimensional random variables, expectations, and covariance matrices are proposed. Physically dimensional counterparts of linear transformations and the multivariate normal distribution are introduced. Four everyday statistical tools are investigated from the point of view of physical dimensions, namely 1) point estimations in linear models, 2) principal components,... (More)  comparatively stringent mathematical frame has been developed, where the behaviour of physical dimensions (like ``length'', ``mass'', and
``time'') and physical units (like 1 m [1 metre], 1 kg [1 kilogramme], and 1 s [1 second]) is modelled. Easytoapply conditions for additivity and multiplicativity of physcial matrices are presented. Precise meanings of physically dimensional random variables, expectations, and covariance matrices are proposed. Physically dimensional counterparts of linear transformations and the multivariate normal distribution are introduced. Four everyday statistical tools are investigated from the point of view of physical dimensions, namely 1) point estimations in linear models, 2) principal components, 3) Fisher's discriminant, and 4) canonical correlations.
The governing idea is the way a mathematically constructed entity transforms when we convert from one collection of physical units to another collection of physical units, e.g. 1 m; 1 kg; 1 s) curvearrowright (1 in; 1 lbavdp; 1 min). When the entity is shown to be indifferent under such a conversion, it will be considered a physical entity, having an intrinsic meaning independent of how we happen to represent it in terms of physical units. (Less)
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https://lup.lub.lu.se/record/933915
 author
 Rikte, Tord ^{LU}
 supervisor

 Björn Holmquist ^{LU}
 organization
 publishing date
 2002
 type
 Thesis
 publication status
 published
 subject
 language
 English
 LU publication?
 yes
 id
 7e8b34a2bc9f4d8e8a40713015ebb3a8 (old id 933915)
 date added to LUP
 20160404 09:22:01
 date last changed
 20181121 20:52:36
@misc{7e8b34a2bc9f4d8e8a40713015ebb3a8, abstract = {{comparatively stringent mathematical frame has been developed, where the behaviour of physical dimensions (like ``length'', ``mass'', and <br/><br> ``time'') and physical units (like 1 m [1 metre], 1 kg [1 kilogramme], and 1 s [1 second]) is modelled. Easytoapply conditions for additivity and multiplicativity of physcial matrices are presented. Precise meanings of physically dimensional random variables, expectations, and covariance matrices are proposed. Physically dimensional counterparts of linear transformations and the multivariate normal distribution are introduced. Four everyday statistical tools are investigated from the point of view of physical dimensions, namely 1) point estimations in linear models, 2) principal components, 3) Fisher's discriminant, and 4) canonical correlations. <br/><br> The governing idea is the way a mathematically constructed entity transforms when we convert from one collection of physical units to another collection of physical units, e.g. 1 m; 1 kg; 1 s) curvearrowright (1 in; 1 lbavdp; 1 min). When the entity is shown to be indifferent under such a conversion, it will be considered a physical entity, having an intrinsic meaning independent of how we happen to represent it in terms of physical units.}}, author = {{Rikte, Tord}}, language = {{eng}}, note = {{Licentiate Thesis}}, title = {{On physical units in multivariate analysis}}, year = {{2002}}, }