{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,29]],"date-time":"2026-06-29T08:55:02Z","timestamp":1782723302182,"version":"3.54.5"},"reference-count":12,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2005,3]]},"abstract":"<jats:p> In this paper we develop a theory for analysing the \"radius\" of the Lie algebra of a matrix Lie group, which is a measure of the size of its commutators. Complete details are given for the Lie algebra \ud835\udd30\ud835\udd2c(n) of skew symmetric matrices where we prove [Formula: see text], X, Y \u2208 \ud835\udd30\ud835\udd2c(n), for the Frobenius norm. We indicate how these ideas might be extended to other matrix Lie algebras. We discuss why these ideas are of interest in applications such as geometric integration and optimal control. <\/jats:p>","DOI":"10.1142\/s0218127405012417","type":"journal-article","created":{"date-parts":[[2005,5,31]],"date-time":"2005-05-31T12:20:40Z","timestamp":1117542040000},"page":"793-801","source":"Crossref","is-referenced-by-count":11,"title":["COMMUTATORS OF SKEW-SYMMETRIC MATRICES"],"prefix":"10.1142","volume":"15","author":[{"given":"ANTHONY M.","family":"BLOCH","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"ARIEH","family":"ISERLES","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, England"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","first-page":"69","volume":"54","author":"Brockett R.","journal-title":"Proc. Symp. Pure Math."},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(94)90203-8"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139172882"},{"key":"rf4","volume-title":"Graphs and Digraphs","author":"Chartrand G.","year":"1986"},{"key":"rf5","volume-title":"Lectures on Ordinary Differential Equations","author":"Hille E.","year":"1969"},{"key":"rf6","volume-title":"Topics in Matrix Analysis","author":"Horn R. A.","year":"1994"},{"key":"rf7","volume-title":"Introduction to Lie Algebras and Representation Theory","author":"Humphreys J. E.","year":"1978"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1017\/S0962492900002154"},{"key":"rf9","volume-title":"Foundations of Differential Geometry","author":"Kobayashi S.","year":"1969"},{"key":"rf10","volume-title":"Introduction to Mechanics and Symmetry","author":"Marsden J. E.","year":"1984"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-1126-6"},{"key":"rf12","first-page":"286","volume":"1","author":"von Neumann J.","journal-title":"Tomsk Univ. Rev."}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127405012417","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T00:06:18Z","timestamp":1565136378000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127405012417"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,3]]},"references-count":12,"journal-issue":{"issue":"03","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2005,3]]}},"alternative-id":["10.1142\/S0218127405012417"],"URL":"https:\/\/doi.org\/10.1142\/s0218127405012417","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2005,3]]}}}