The Approximation of One Matrix by Another of Lower Rank Carl Eckart and Gale Young
نویسندگان
چکیده
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 do~vn, 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.
منابع مشابه
A Counterexample to the Possibility of an Extension of the Eckart-Young Low-Rank Approximation Theorem for the Orthogonal Rank Tensor Decomposition
Earlier work has shown that no extension of the Eckart–Young SVD approximation theorem can be made to the strong orthogonal rank tensor decomposition. Here, we present a counterexample to the extension of the Eckart–Young SVD approximation theorem to the orthogonal rank tensor decomposition, answering an open question previously posed by Kolda [SIAM J. Matrix Anal. Appl., 23 (2001), pp. 243–355].
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