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The Approximation of One Matrix by Another of Lower Rank
Abstract
The mathematical problem of approximating one matrix by another of lower rank is closely related to the fundamental postulate of factor-theory. When formulated as a least-squares problem, the normal equations cannot be immediately written down, since the elements of the approximate matrix are not independent of one another. The solution of the problem is simplified by first expressing the matrices in a canonic form. It is found that the problem always has a solution which is usually unique. Several conclusions can be drawn from the form of this solution. A hypothetical interpretation of the canonic components of a score matrix is discussed.
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Citations
Cited by
Abdi, H., & Williams, L. J. (2010) · WIREs Computational Statistics · doi:10.1002/wics.101 · Cited by 11,104
Some Mathematical Notes on Three-Mode Factor Analysis
Tucker, L. R. (1966) · Psychometrika · doi:10.1007/bf02289464 · Cited by 3,492
Generalized procrustes analysis
Gower, J. C. (1975) · Psychometrika · doi:10.1007/bf02291478 · Cited by 3,267
Demene, C., Deffieux, T., Pernot, M., Osmanski, B.-F., Biran, V., Gennisson, J.-L., Sieu, L.-A., Bergel, A., Franqui, S., Correas, J.-M., et al. (2015) · IEEE Transactions on Medical Imaging · doi:10.1109/tmi.2015.2428634 · Cited by 983
Evolutionary Personality Psychology
Buss, D. M. (1991) · Annual Review of Psychology · doi:10.1146/annurev.ps.42.020191.002331 · Cited by 930
Metadata
- Authors
- Eckart, C., & Young, G.
- Venue
- Psychometrika
- Publisher
- Cambridge University Press (CUP)
- Published
- 1936-09
- Volume
- 1
- Issue
- 3
- Pages
- 211-218
- ISSN
- 0033-3123 (ISSN-L)
- 1860-0980
- OpenAlex
- W2004026774
- Cited by
- 3,800
- References
- 0
- FWCI
- 6.11
- Type
- journal article
- Language
- en
- Open access
- closed
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- Eckart, C., & Young, G. (1936). The Approximation of One Matrix by Another of Lower Rank. Psychometrika. https://doi.org/10.1007/bf02288367
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