| 000 | 02970nam a22004575i 4500 | ||
|---|---|---|---|
| 001 | 978-1-4419-9887-3 | ||
| 003 | DE-He213 | ||
| 005 | 20140220083731.0 | ||
| 007 | cr nn 008mamaa | ||
| 008 | 110406s2011 xxu| s |||| 0|eng d | ||
| 020 |
_a9781441998873 _9978-1-4419-9887-3 |
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| 024 | 7 |
_a10.1007/978-1-4419-9887-3 _2doi |
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| 050 | 4 | _aQA276-280 | |
| 072 | 7 |
_aPBT _2bicssc |
|
| 072 | 7 |
_aMAT029000 _2bisacsh |
|
| 082 | 0 | 4 |
_a519.5 _223 |
| 100 | 1 |
_aYanai, Haruo. _eauthor. |
|
| 245 | 1 | 0 |
_aProjection Matrices, Generalized Inverse Matrices, and Singular Value Decomposition _h[electronic resource] / _cby Haruo Yanai, Kei Takeuchi, Yoshio Takane. |
| 264 | 1 |
_aNew York, NY : _bSpringer New York, _c2011. |
|
| 300 |
_aXII, 236 p. _bonline resource. |
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| 336 |
_atext _btxt _2rdacontent |
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| 337 |
_acomputer _bc _2rdamedia |
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| 338 |
_aonline resource _bcr _2rdacarrier |
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| 347 |
_atext file _bPDF _2rda |
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| 490 | 1 | _aStatistics for Social and Behavioral Sciences | |
| 505 | 0 | _aFundamentals of Linear Algebra -- Projection Matrices -- Generalized Inverse Matrices -- Explicit Representations -- Singular Value Decomposition (SVD) -- Various Applications. | |
| 520 | _aAside from distribution theory, projections and the singular value decomposition (SVD) are the two most important concepts for understanding the basic mechanism of multivariate analysis. The former underlies the least squares estimation in regression analysis, which is essentially a projection of one subspace onto another, and the latter underlies principal component analysis, which seeks to find a subspace that captures the largest variability in the original space. This book is about projections and SVD. A thorough discussion of generalized inverse (g-inverse) matrices is also given because it is closely related to the former. The book provides systematic and in-depth accounts of these concepts from a unified viewpoint of linear transformations finite dimensional vector spaces. More specially, it shows that projection matrices (projectors) and g-inverse matrices can be defined in various ways so that a vector space is decomposed into a direct-sum of (disjoint) subspaces. Projection Matrices, Generalized Inverse Matrices, and Singular Value Decomposition will be useful for researchers, practitioners, and students in applied mathematics, statistics, engineering, behaviormetrics, and other fields. | ||
| 650 | 0 | _aStatistics. | |
| 650 | 1 | 4 | _aStatistics. |
| 650 | 2 | 4 | _aStatistics, general. |
| 650 | 2 | 4 | _aStatistics for Life Sciences, Medicine, Health Sciences. |
| 700 | 1 |
_aTakeuchi, Kei. _eauthor. |
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| 700 | 1 |
_aTakane, Yoshio. _eauthor. |
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| 710 | 2 | _aSpringerLink (Online service) | |
| 773 | 0 | _tSpringer eBooks | |
| 776 | 0 | 8 |
_iPrinted edition: _z9781441998866 |
| 830 | 0 | _aStatistics for Social and Behavioral Sciences | |
| 856 | 4 | 0 | _uhttp://dx.doi.org/10.1007/978-1-4419-9887-3 |
| 912 | _aZDB-2-SMA | ||
| 999 |
_c106147 _d106147 |
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