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Cayley–Hamilton theorem
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== References == *{{cite journal|first1=Y.|last1=Alagös|first2=K.|last2=Oral|first3=S.|last3=Yüce|title=Split Quaternion Matrices| journal=Miskolc Mathematical Notes|issn=1787-2405|volume=13|issue=2|year=2012|pages=223–232| postscript=none| doi=10.18514/MMN.2012.364|doi-access=free}} (open access) *{{citation|last1 = Atiyah|first1 = M. F.|author1-link = M. F. Atiyah|last2 = MacDonald|first2 = I. G.|author2-link = I. G. Macdonald | year = 1969|title = Introduction to Commutative Algebra|publisher = Westview Press|isbn=978-0-201-40751-8}} *{{cite journal|first1=A. O.|last1=Barut|authorlink1=Asım Orhan Barut|first2=J. R.|last2=Zeni|first3=A.|last3=Laufer| journal=J. Phys. A: Math. Gen.|volume=27|pages=5239–5250|doi=10.1088/0305-4470/27/15/022|title=The exponential map for the conformal group O(2,4)|year=1994a|issue=15|arxiv=hep-th/9408105|bibcode = 1994JPhA...27.5239B }} *{{cite journal|first1=A. O.|last1=Barut|authorlink1=Asım Orhan Barut|first2=J. R.|last2=Zeni|first3=A.|last3=Laufer | journal=J. Phys. A: Math. Gen.|volume=27|issue=20|pages=6799–6806|doi=10.1088/0305-4470/27/20/017|title=The exponential map for the unitary group SU(2,2)|year=1994b|arxiv=hep-th/9408145|bibcode = 1994JPhA...27.6799B | s2cid=16495633}} *{{cite book|last=Bhatia|first=R.|year=1997|title=Matrix Analysis|publisher=Springer|series=Graduate texts in mathematics| volume=169|isbn=978-0387948461}} *{{cite book|last= Brown|first= Lowell S. |title= Quantum Field Theory |publisher= [[Cambridge University Press]] |year= 1994|isbn= 978-0-521-46946-3 }} *{{cite journal|first=A.|last=Cayley|title=A Memoir on the Theory of Matrices|journal=Philos. Trans. |year=1858 |volume=148 |authorlink=Arthur Cayley}} *{{cite book|first=A.|last=Cayley|title=The Collected Mathematical Papers of Arthur Cayley|volume=2|publisher=Forgotten books |year=1889|asin=B008HUED9O|series=(Classic Reprint)}} *{{cite journal|last=Crilly|first=T.|journal=Notes Rec. R. Soc. Lond.|volume=52|year=1998|issue=2|pages=267–282|title=The young Arthur Cayley|doi=10.1098/rsnr.1998.0050|s2cid=146669911}} *{{cite journal|last1=Curtright|first1 = T L |last2=Fairlie|first2= D B|last3=Zachos|first3 = C K|year = 2014|title = A compact formula for rotations as spin matrix polynomials| journal =SIGMA| volume=10|issue=2014| page=084 | doi=10.3842/SIGMA.2014.084 |authorlink=David Fairlie|authorlink2=Thomas Curtright|authorlink3=Cosmas Zachos|arxiv =1402.3541 | bibcode=2014SIGMA..10..084C|s2cid=18776942}} *{{cite journal|first=G.|last=Frobenius|title=Ueber lineare Substutionen und bilineare Formen|journal=J. Reine Angew. Math. |volume=1878|issue=84|year=1878|pages=1–63|authorlink=Ferdinand Georg Frobenius|doi=10.1515/crll.1878.84.1|doi-broken-date=2 January 2025 }} *{{cite book| last= Gantmacher|first=F.R. | title=The Theory of Matrices |year=1960| publisher= Chelsea Publishing | location= NY | isbn = 978-0-8218-1376-8 }} * {{Citation|last1=Gatto|first1=Letterio|last2=Salehyan|first2=Parham|title=Hasse–Schmidt derivations on Grassmann algebras |publisher=Springer|year=2016|isbn=978-3-319-31842-4|mr=3524604|doi=10.1007/978-3-319-31842-4}} * {{citation|title=Remarks on the Cayley-Hamilton Theorem |year=2015 |first1=Letterio |last1=Gatto |first2=Inna |last2=Scherbak |arxiv=1510.03022 }} *{{cite book| last= Garrett|first=Paul B. | title=Abstract Algebra |year=2007| publisher= Chapman and Hall/CRC |location= NY | isbn = 978-1584886891 }} *{{cite book|first=W. R.|last=Hamilton|title=Lectures on Quaternions|url=https://archive.org/details/bub_gb_TCwPAAAAIAAJ |location=Dublin|year=1853|authorlink=William Rowan Hamilton}} *{{cite journal|first=W. R.|last=Hamilton|title=On a New and General Method of Inverting a Linear and Quaternion Function of a Quaternion|journal=[[Proceedings of the Royal Irish Academy]]|volume=viii|year=1864a|pages=182–183}} (communicated on June 9, 1862) *{{cite journal|first=W. R.|last=Hamilton|title=On the Existence of a Symbolic and Biquadratic Equation, which is satisfied by the Symbol of Linear Operation in Quaternions|journal=[[Proceedings of the Royal Irish Academy]]| volume=viii| year=1864b| pages=190–101}} (communicated on June 23, 1862) *{{cite journal|first=S. H.|last=Hou|title=Classroom Note: A Simple Proof of the Leverrier--Faddeev Characteristic Polynomial Algorithm|journal=SIAM Review|doi=10.1137/S003614459732076X| volume=40 | issue=3| year=1998| pages=706–709| bibcode=1998SIAMR..40..706H}} [http://epubs.siam.org/doi/pdf/10.1137/S003614459732076X "Classroom Note: A Simple Proof of the Leverrier--Faddeev Characteristic Polynomial Algorithm"] *{{cite journal|first=W. R.|last=Hamilton|title=On the Existence of a Symbolic and Biquadratic Equation which is satisfied by the Symbol of Linear or Distributive Operation on a Quaternion|journal=[[Philosophical Magazine|The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science]]|issn=1478-6435|volume=24|series= series '''iv'''| year=1862| pages=127–128| url=http://zs.thulb.uni-jena.de/rsc/viewer/jportal_derivate_00126615/PMS_1862_Bd24_%200135.tif|access-date=2015-02-14}} *{{cite book|first=Alston S.|last=Householder|title=The Theory of Matrices in Numerical Analysis |publisher=Dover Books on Mathematics|year=2006|authorlink=Alston Scott Householder | isbn=978-0486449722}} * {{cite arXiv | last = Krivoruchenko | first=M. I. | date=2016 | title=Trace Identities for Skew-Symmetric Matrices | class=math-ph | eprint = 1605.00447}} * {{cite journal | last1 = Kondratyuk | first1 = L. A. | last2 = Krivoruchenko | first2 = M. I. | year = 1992 | title = Superconducting quark matter in SU(2) color group | journal = Zeitschrift für Physik A | volume = 344 | issue = 1| pages = 99–115 | doi = 10.1007/BF01291027 | bibcode = 1992ZPhyA.344...99K | s2cid = 120467300 }} *{{cite journal|first=A.|last=Laufer|journal=J. Phys. A: Math. Gen.|volume=30|issue=15|pages=5455–5470| doi=10.1088/0305-4470/30/15/029 | title=The exponential map of GL(N)|year=1997|arxiv=hep-th/9604049|bibcode = 1997JPhA...30.5455L |s2cid=10699434}} *{{cite journal|last=Tian|first=Y.|title=Matrix representations of octonions and their application| doi=10.1007/BF03042010| journal=[[Advances in Applied Clifford Algebras]]|issn=0188-7009|volume=10|issue=1|year=2000|pages=61–90| arxiv=math/0003166 | bibcode=2000math......3166T|citeseerx=10.1.1.237.2217|s2cid=14465054}} *{{cite journal|last1=Zeni|first1=J. R.|first2=W.A.|last2=Rodrigues|title=A thoughtful study of Lorentz transformations by Clifford algebras|journal=Int. J. Mod. Phys. A|volume=7|issue=8|pages=1793 pp|year=1992|doi= 10.1142/S0217751X92000776 | bibcode = 1992IJMPA...7.1793Z }} *{{cite journal|last=Zhang|first=F.|title=Quaternions and matrices of quaternions|journal=Linear Algebra and Its Applications | issn=0024-3795|volume=251|year=1997|pages=21–57| doi=10.1016/0024-3795(95)00543-9 | postscript=none|doi-access=free}} (open archive).
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