کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
1180964 | 1491549 | 2013 | 5 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Direct transformations yielding the knight's move pattern in 3Â ÃÂ 3Â ÃÂ 3 arrays
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موضوعات مرتبط
مهندسی و علوم پایه
شیمی
شیمی آنالیزی یا شیمی تجزیه
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: Direct transformations yielding the knight's move pattern in 3Â ÃÂ 3Â ÃÂ 3 arrays Direct transformations yielding the knight's move pattern in 3Â ÃÂ 3Â ÃÂ 3 arrays](/preview/png/1180964.png)
چکیده انگلیسی
Three-way arrays (or tensors) can be regarded as extensions of the traditional two-way data matrices that have a third dimension. Studying algebraic properties of arrays is relevant, for example, for the Tucker three-way PCA method, which generalizes principal component analysis to three-way data. One important algebraic property of arrays is concerned with the possibility of transformations to simplicity. An array is said to be transformed to a simple form when it can be manipulated by a sequence of invertible operations such that a vast majority of its entries become zero. This paper shows how 3Â ÃÂ 3Â ÃÂ 3 arrays, whether symmetric or nonsymmetric, can be transformed to a simple form with 18 out of its 27 entries equal to zero. We call this simple form the “knight's move pattern” due to a loose resemblance to the moves of a knight in a game of chess. The pattern was examined by Kiers, Ten Berge, and Rocci. It will be shown how the knight's move pattern can be found by means of a numeric-algebraic procedure based on the Gröbner basis. This approach seems to work almost surely for randomly generated arrays, whether symmetric or nonsymmetric.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Chemometrics and Intelligent Laboratory Systems - Volume 129, 15 November 2013, Pages 10-14
Journal: Chemometrics and Intelligent Laboratory Systems - Volume 129, 15 November 2013, Pages 10-14
نویسندگان
Jorge N. Tendeiro, Jos M.F. Ten Berge, Vartan Choulakian,