The Approximation of One Matrix by Another of Lower Rank¶
Eckart, C., & Young, G. (1936). The Approximation of One Matrix by Another of Lower Rank. Psychometrika, 1(3), 211-218.
Cited by¶
2 citations across 2 artifacts.
Each citation links to the sentence it supports in the citing article.
Mechanisms¶
- Singular Value Decomposition
- Its strength is generality: SVD applies to any matrix — square or not, normal or not — and the truncated SVD is the mathematically optimal low-rank approximation
This sourceEstablishes the optimal least-squares lower-rank matrix approximation result now expressed through truncating the singular-value decomposition.
- Its strength is generality: SVD applies to any matrix — square or not, normal or not — and the truncated SVD is the mathematically optimal low-rank approximation
- Singular-Value Rank Diagnosis
- Its strength is authority: singular values are the rotation-invariant, definitive measure of independent content, and by the Eckart–Young theorem
This sourceProves the exact least-squares error of the optimal lower-rank matrix approximation from the omitted canonical components.
- Its strength is authority: singular values are the rotation-invariant, definitive measure of independent content, and by the Eckart–Young theorem
Verification¶
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Registry ID ref:ffb837dde094 · see in the full table