C. Jordan, \Essai sur la geometrie a n dimensions", Bulletin de la Societe Mathematique 3, 103-174, 1875. Home/Search Document Not in Database Summary Related Articles Check |
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Canonical Correlations between Input and Output Processes of .. - De Cock, De Moor (Correct)
....is uncorrelated with the future inputs, translates to lim j## X p U lim j## X f U and lim Y p U f = 0 , 2.19) respectively. 5 3 Principal angles between and principal directions in subspaces The concept of principal angles between subspaces of linear vector spaces is due to Jordan [13] in the 19th century. In the area of systems and control, the principal angles between and the principal directions in two subspaces are used in subspace identification methods [22] and also in model updating [7] and damage location [8] In the latter two applications, one starts from a finite ....
C. Jordan, "Essai sur la geometrie a n dimensions", Bulletin de la Societe Mathematique 3, 103--174, 1875.
Subspace angles and distances between ARMA models - De Cock, De Moor (2000) (4 citations) (Correct)
....we give their relation to different distance measures for ARMA models. Most attention is paid to a recently defined metric for ARMA models that is based on the cepstra of the models involved. 1 Introduction The concept of principal angles between subspaces of linear vector spaces is due to Jordan [11] in the previous century. This notion was translated into the statistical notion of canonical correlations by Hotelling [10] Applications include data analysis [6] random processes [5] 12] and stochastic realization [1] 3] 15] and references herein) Numerically stable methods to compute the ....
Jordan C. Essai sur la g eom etrie a n dimensions. Bulletin de la Societe Mathematique, Vol.3, pp.103--174, 1875.
Subspace Angles between AR Models - De Cock, De Moor (2000) (Correct)
....and Technological Research in Industry) Bart De Moor is a Research Associate with the F.W.O. Fund for Scientific ResearchFlanders) and professor extra ordinary at the K.U.Leuven. 1 I. Introduction The concept of principal angles between subspaces of linear vector spaces is due to Jordan [1] in the previous century. This notion was translated into the statistical notion of canonical correlations by Hotelling [2] Applications include data analysis [3] random processes [4] 5] and stochastic realization [6] 7] 8] and references herein) Numerically stable methods to compute the ....
C. Jordan, "Essai sur la g'eom'etrie `a n dimensions," Bulletin de la Soci'et'e Math'ematique, vol. 3, pp. 103--174, 1875.
Distance And Parallelism Between Flats In R n - DuPre, Kass (1992) (Correct)
....DISTANCE, PARALLELISM AND ORTHOGONAL PROJECTION It is rather surprising that a formula for the distance between flats in IR n , which is a natural generalization of the classical ones for the distance between lines in IR 3 , or between points in IR n , apparently does not exist. Jordan, in [J], p.138 , purports to derive the general formula, but, as we shall indicate, this formula only works in the special case that the two flats are what we call totally skew. We use terminology and notation from [S] except for the following change: we write Row(A) Col(A) for the row respectively ....
....) v u u t ka Gamma bk 2 Gamma k s A t A A t B B t A B t B Gamma1 A t B t (a Gamma b)k 2 : 10 ARTHUR M. DUPR E SEYMOUR KASS Proof. Notice that L 1 Gamma L 2 = A B ) a Gamma b and apply the previous lemma. This formula is similar to that of Jordan in [J], p.144 , under the same assumptions, which are equivalent to L 1 ; L 2 being totally skew, as in theorem 5. Finally, as motivation for our treating yet one more case, it should be mentioned that the classical formula for the distance between a point and a hyperplane in IR n assumes mixed data ....
C. Jordan, Essai sur la g'eom'etrie `a n dimensions, Paris, Bull. Soc. Math. 3 (1875), 103---174.
Canonical Correlations between Input and Output Processes of .. - De Cock, De Moor (2002) (Correct)
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C. Jordan, \Essai sur la geometrie a n dimensions", Bulletin de la Societe Mathematique 3, 103-174, 1875.
Subspace Angles between ARMA Models - De Cock, De Moor (2002) (Correct)
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C. Jordan, Essai sur la geometrie a n dimensions, Bulletin de la Societe Mathematique 3 (1875) 103-174.
Subspace Angles for Fault Detection - De Cock, De Moor (2002) (Correct)
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C. Jordan, Essai sur la g eom etrie a n dimensions, Bulletin de la Societe Mathematique, Vol. 3 (1875), pp. 103--174.
Subspace Algorithms for the Stochastic Identification Problem - Van Overschee, De Moor (20 citations) (Correct)
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Jordan C. Essai sur la g'eometrie `a n dimensions. Bull. Soc. Math. France, 3, 1875, pp. 103-174.
On the geometry of complex Grassmann manifold, its noncompact.. - Berceanu (1997) (Correct)
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C. Jordan, "Essai sur la Geometrie a n dimensions", Bull. Soc. Math. France t. lll 103 (1875), in OEuvres de C. Jordan, Paris, Gauthier-Villars, Tome III 79 (1962).
Subspace Algorithms for the Stochastic Identification Problem - Van Overschee, De Moor (1993) (20 citations) (Correct)
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Jordan C. (1875). Essai sur la g'eometrie `a n dimensions. Bull. Soc. Math. France, 3, 103-174. Kung S.Y. (1978). A New Identification and Model Reduction Algorithm via Singular Value Decomposition. Proceedings of the 12th Asilomar Conference on Circuits, Systems and Computers, Pacific Grove, 705-714.
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