The Approximation of One Matrix by Another of Lower Rank
Bibliographic Data
| ID | 23324316 |
|---|---|
| Authors | Carl Eckart (University of Chicago), Gale Young (University of Chicago) |
| Year | 1936 |
| Volume | 1 |
| Issue | 3 |
| Pages | 211-218 |
| Publication date | 1936-09-01 |
| Peer Reviewed | Yes |
| Open Access | Yes |
| Type | ARTICLE |
| Venue | Psychometrika (JOURNAL) |
| Journal identifiers | ISSN: 0033-3123 • E-ISSN: 1860-0980 |
| Publisher | Cambridge University Press (CUP) (PUBLISHER) |
| DOI | 10.1007/bf02288367 |
| OpenAlex | W2004026774 |
| Language | EN |
| Citations received | 84 |
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.
Algebra over a field · Calculus (dental) · Combinatorics · Interpretation (philosophy) · Low-rank approximation · Matrix (chemical analysis) · Pure mathematics · Rank (graph theory) · Applied Mathematics · Computer Science · Mathematics · Matrix Theory and Algorithms
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| Unique citing works | 84 |
|---|---|
| Citations per year | 1,33 |
| Citation span | 1963 - 2025 (63) |
| Citation velocity | recent |
| Highly cited | No |
| Citation types | Neutral: 70 |