Adjugate matrix: Difference between revisions

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Fix {{citation needed}}. Adjunct really is sort of an outdated term, based on searching google scholar.
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In [[linear algebra]], the '''adjugate''' or '''classical adjoint''' of a [[square matrix]] is the [[transpose]] of its [[cofactor matrix]].<ref>{{cite book |first=F. R. |last=Gantmacher |authorlink=Felix Gantmacher |title=The Theory of Matrices |volume=1 |publisher=Chelsea |___location=New York |year=1960 |isbn=0-8218-1376-5 |pages=76–89 |url=https://books.google.com/books?id=ePFtMw9v92sC&pg=PA76 }}</ref> It is also occasionally known as '''adjunct matrix''',<ref>{{cite journal|author1=Claeyssen, J.C.R.|year=1990|title=On predicting the response of non-conservative linear vibrating systems by using dynamical matrix solutions|journal=Journal of Sound and Vibration|volume=140|issue=1|pppages=7373–84|doi=10.1016/0022-460X(90)90907-84H}}</ref><ref>{{cite journal|author1=Chen, W.|author2=Chen, W.|author3=Chen, Y.J.|year=2004|title=A characteristic matrix approach for analyzing resonant ring lattice devices|journal=IEEE Photonics Technology Letters|volume=16|issue=2|pppages=458-460458–460|doi=10.1109/LPT.2003.823104}}</ref> though this nomenclature appears to have decreased in usage.
 
The adjugate<ref>{{cite book | last=Strang | first=Gilbert | authorlink=Gilbert Strang | title=Linear Algebra and its Applications | edition=3rd | year=1988 | publisher=Harcourt Brace Jovanovich | isbn=0-15-551005-3 | pages=[https://archive.org/details/linearalgebraits00stra/page/231 231–232] | chapter=Section 4.4: Applications of determinants | chapter-url-access=registration | chapter-url=https://archive.org/details/linearalgebraits00stra/page/231 }}</ref> has sometimes been called the "adjoint",<ref>{{cite book|ref=harv|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=0-486-44972-6 |pages=166–168 }}</ref> but today the "adjoint" of a matrix normally refers to its corresponding [[Hermitian adjoint|adjoint operator]], which is its [[conjugate transpose]].
 
== Definition ==