The Approximation of One Matrix by Another of Lower Rank  

Oleh:

Eckart, Carl ; Young, Gale

Jenis: Article from Journal - e-Journal
Dalam koleksi: Psychometrika: A Journal of Quantitative Psychology vol. 1 no. 3 (Sep. 1936), page 211-218.
Topik: Approximation; Matrix; Preliminary Theorems; Canonic Components of ß
Fulltext: The Approximation of One Matrix by Another of Lower Rank.pdf (342.82KB)

Isi artikel

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.

Opini Anda

Klik untuk menuliskan opini Anda tentang koleksi ini!

Kembali