Compound matrix: Difference between revisions

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In [[linear algebra]], a branch of [[mathematics]], a ('''multiplicative''') '''compound matrix''' is a [[matrix (mathematics)|matrix]] whose entries are all minors, of a given size, of another matrix.<ref>Horn, Roger A. and Johnson, Charles R., ''Matrix Analysis'', 2nd edition, Cambridge University Press, 2013, {{isbn|978-0-521-54823-6}}, p. 21</ref><ref name=":0">{{Cite journal|last=Muldowney|first=James S.|date=1990|title=Compound matrices and ordinary differential equations|url=http://projecteuclid.org/euclid.rmjm/1181073047|journal=Rocky Mountain Journal of Mathematics|language=en|volume=20|issue=4|pages=857–872|doi=10.1216/rmjm/1181073047|issn=0035-7596|via=}}</ref> Compound matrices are closely related to [[exterior algebra]]s.

== Definition ==

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== Applications ==

The computation of compound matrices appears in a wide array of problems.<ref>{{cite techreport|first=Boutin|last=D.L.|author2=R.F. Gleeson|author3=R.M. Williams|title=Wedge Theory / Compound Matrices: Properties and Applications.|institution=Office of Naval Research|url=httphttps://handleapps.dtic.mil/100.2sti/pdfs/ADA320264.pdf|year=1996|number=NAWCADPAX–96-220-TR}}</ref><ref name=":0" />

Compound and adjugate matrices appear when computing determinants of linear combinations of matrices. It is elementary to check that, if {{math|''A''}} and {{math|''B''}} are {{math|''n'' × ''n''}} matrices, then