Revision as of 15:54, 5 October 2018 edit Fma1201 (talk \| contribs) 12 edits →Relation to adjugate matrices: I^c and J_c must be exchanged in the definition of the r^th higher adjugate matrix, as well as in the Jacobi's formula ← Previous edit		Revision as of 02:48, 12 March 2019 edit undo Rgdboer (talk \| contribs) Autopatrolled, Extended confirmed users, Pending changes reviewers 18,124 edits →Properties: cite Flanders on Sylvester-Franke thm Next edit →
Line 76: ** Normal. * If {{math\|''A''}} is invertible, then so is {{math\|''C''<sub>''r''</sub>(''A'')}}, and {{math\|1=''C''<sub>''r''</sub>(''A''{{i sup\|−1}}) = ''C''<sub>''r''</sub>(''A''){{i sup\|−1}}}}. * (Sylvester–Franke theorem) If {{math\|1 ≤ ''r'' ≤ ''n''}}, then <math>\det C_r(A) = (\det A)^{\binom{n-1}{r-1}}</math>.<ref name="Tornheim1952">{{cite journal\|last1=Tornheim\|first1=Leonard\|title=The ~~Sylvester-Franke~~Sylvester–Franke Theorem\|journal=The American Mathematical Monthly\|volume=59\|issue=6\|year=1952\|pages=389\|issn=00029890\|doi=10.2307/2306811}}</ref><ref>[[Harley Flanders]] (1953) "A Note on the Sylvester-Franke Theorem", [[American Mathematical Monthly]] 60: 543–5, {{mr\|id=0057835}}</ref> ==Relation to exterior powers==

Compound matrix: Difference between revisions