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Orthogonal matrix
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==References== <!-- Using [[WP:CITET]] --> * {{citation | last1 = Diaconis | first1 = Persi | author-link1 = Persi Diaconis | first2 = Mehrdad |last2= Shahshahani | title = The subgroup algorithm for generating uniform random variables | journal = Probability in the Engineering and Informational Sciences | volume = 1 | pages = 15–32 | year = 1987 | issn = 0269-9648 | doi = 10.1017/S0269964800000255 | s2cid = 122752374 }} * {{citation | last= Dubrulle | first=Augustin A. | title = An Optimum Iteration for the Matrix Polar Decomposition | journal = Electronic Transactions on Numerical Analysis | volume = 8 | pages = 21–25 | year = 1999 | url = http://etna.mcs.kent.edu/}} * {{citation | last1 = Golub | first1 = Gene H. | author-link1 = Gene H. Golub | first2 = Charles F.|last2=Van Loan|author-link2=Charles F. Van Loan | title = Matrix Computations | edition = 3/e | publisher = Johns Hopkins University Press | year = 1996 | location = Baltimore | isbn = 978-0-8018-5414-9 }} * {{citation | last = Higham | first = Nicholas | author-link = Nicholas Higham | title = Computing the Polar Decomposition—with Applications | journal = SIAM Journal on Scientific and Statistical Computing | volume = 7 | issue = 4 | pages = 1160–1174 | year = 1986 | issn = 0196-5204 | doi = 10.1137/0907079 | url = http://eprints.maths.manchester.ac.uk/694/1/high86p.pdf }} * {{citation | last1 = Higham | first1 = Nicholas | author-link1 = Nicholas Higham | first2 = Robert |last2=Schreiber | title = Fast polar decomposition of an arbitrary matrix | journal = SIAM Journal on Scientific and Statistical Computing | volume = 11 | issue = 4 | pages = 648–655 | date = July 1990 | issn = 0196-5204 | doi = 10.1137/0911038 | citeseerx = 10.1.1.230.4322 | s2cid = 14268409 }} [https://web.archive.org/web/20051016153437/http://www.ma.man.ac.uk/~higham/pap-mf.html] * {{citation | last = Stewart | first = G. W. | author-link = G. W. Stewart | title = The Economical Storage of Plane Rotations | journal = Numerische Mathematik | volume = 25 | issue = 2 | pages = 137–138 | year = 1976 | doi = 10.1007/BF01462266 | s2cid = 120372682 | issn = 0029-599X }} * {{citation | last = Stewart | first = G. W. | author-link = G. W. Stewart | title = The Efficient Generation of Random Orthogonal Matrices with an Application to Condition Estimators | journal = SIAM Journal on Numerical Analysis | volume = 17 | issue = 3 | pages = 403–409 | year = 1980 | issn = 0036-1429 | doi = 10.1137/0717034 | bibcode = 1980SJNA...17..403S }} * {{citation | last = Mezzadri | first = Francesco | title = How to generate random matrices from the classical compact groups | journal = Notices of the American Mathematical Society | volume = 54 | year = 2006 | arxiv = math-ph/0609050 | bibcode = 2006math.ph...9050M }} <!-- * [[Persi Diaconis]], Mehrdad Shahshahani. The subgroup algorithm for generating uniform random variables. '' Prob. in Eng. and Info. Sci.'', vol. 1, 15–32, 1987. {{issn|0269-9648}}. * Augustin A. Dubrulle. ''Frobenius Iteration for the Matrix Polar Decomposition''. HP Labs Technical Report HPL-94-117. December 16, 1994. [http://www.hpl.hp.com/techreports/94/HPL-94-117.html] * [[Gene H. Golub]], [[Charles F. Van Loan]]. ''Matrix Computations, 3/e''. Johns Hopkins University Press, Baltimore, 1996. {{isbn|978-0-8018-5414-9}}. * [[Nicholas Higham]]. Computing the Polar Decomposition—with Applications. ''SIAM Journal on Scientific and Statistical Computing'', 7(4):1160–1174, 1986. {{issn|0196-5204}}. [http://locus.siam.org/SISC/volume-07/art_0907079.html] * {{citation|first1=Nicholas|last1=Higham|authorlink2=Nicholas Higham|first2=Robert|last2=Schreiber|title=Fast polar decomposition of an arbitrary matrix|journal=SIAM Journal on Scientific and Statistical Computing|volume=11|issue=4|pages=648–655|year=1990|url=http://locus.siam.org/SISC/volume-11/art_0911038.html|doi=10.1137/0911038}}; [http://www.ma.man.ac.uk/~higham/pap-mf.html]. * {{citation|first=G. W.|last=Stewart|title=The Economical Storage of Plane Rotations|journal=Numerische Mathematik|volume=25|issue=2|pages=137–138|year=1976|doi=10.1007/BF01462266}}. * {{citation|first=G. W.|last=Stewart|title=The Efficient Generation of Random Orthogonal Matrices with an Application to Condition Estimation|journal=SIAM J. Numer. Anal.|volume=17|issue=3|pages=403–409|year=1980|doi=10.1137/0717034}}. -->
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