Kompendium til lineÃ¦r Algebra - bennike.org

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Kompendium til Lineæ r Algebra Politstudiet, matematik, 1. årsprøve Af Erik Bennike Hvis man fx skal afgøre om en 5 × 5 matrix er negativ definit tager de tilhørende ledende hovedunderdeterminanter. Så skal de ledende underdeterminanter have følgende fortegn: 1 × 1 2 × 2 3 × 3 4 × 4 5 × 5 (–1) 1 = –1, dvs. ± (–1) 2 = 1, dvs. (–1) 3 = –1, dvs. ± (–1) 4 = 1, dvs. (–1) 5 = –1, dvs. ± Sæ tn.: 'HWHUPLQDQWHQ DI HQ V\PPHWULVN PDWUL[ Determinanten af en symmetrisk matrix er lig med produktet af egenvæ rdierne. - 37 -
Kompendium til Lineæ r Algebra Politstudiet, matematik, 1. årsprøve Af Erik Bennike Oversigtsopgave til Lineæ r Algebra v/ Arne Frøsig Rasmussen 9L VWDUWHU PHG DW GHILQHUH HQ PDWUL[ $ %HUHJQ GHWHUPLQDQWHQ DI $ 9L /DSODFHXGYLNOHU HIWHU V¡MOH ⎛2 ⎜ $ = ⎜0 ⎜ ⎝4 2 0 4 2 4 det $ = 0 6 0 = 6⋅ = 6⋅ − 4 2 4 0 2 %HVWHP UDQJHQ DI PDWUL[ $ 0 6 0 ( 4 −16) = 72 'D GHW $ HU $ UHJXO U (UJR KDYHV UJ $ - 38 - 4⎞ ⎟ 0⎟ 2⎟ ⎠ (U PDWUL[ $ UHJXO U" $QJLY L EHNU IWHQGH $� IDOG -D $ HU UHJXO U MI VS¡UJVPnO 9L $� XGUHJQHU ( $ ( � ) ⎛1 ⎜ ⎜0 ⎜ ⎝0 0 1 0 ⎛2 ⎜ = ⎜0 ⎜ ⎝4 0 0 1 − 0 1 3 0 6 0 1 6 4 0 2 0 1 6 0 1 0 0 0 1 0 1 3 ⎞ ⎟ 0 ⎟ 1 − ⎟ 6 ⎠ 0⎞ ⎟ 0⎟ 1 ⎟ ⎠ − 2 * * 1 2 1 6 ⎛1 ⎜ ⎜0 ⎜ ⎝0 � 0 1 0 � 2 0 1 2 0 − 6 − 2 � 6nOHGHV VHV GHW LJHQ DW KDU HQ $� LQYHUV PDWUL[ GHU HU JLYHW YHG $ −1 ⎛− ⎜ = ⎜ 0 ⎜ 1 ⎝ 3 1 6 0 1 6 0 1 3 ⎞ ⎟ 0 ⎟ 1 − ⎟ 6 ⎠ $� 9L NRQWUROOHUHU DW $ Â ⎛2 ⎜ −1 $ ⋅ $ = ⎜0 ⎜ ⎝4 0 6 0 1 4⎞ ⎛− 6 ⎟ ⎜ 0⎟ ⋅⎜ 0 2⎟ ⎜ 1 ⎠ ⎝ 3 0 � (� 0 1 3 ⎞ ⎛1 ⎟ ⎜ 0 ⎟ = ⎜0 1 − ⎟ ⎜ 6 ⎠ ⎝0 � NRQWURO $� HU 2. HU NRUUHNW XGUHJQHW 1 6 0 1 0 0⎞ ⎟ 0⎟ 1⎟ ⎠ 0 1 6 0 0⎞ ⎟ 0⎟ 1 ⎟ ⎠ 1 3 * − 1 6
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Kompendium til lineÃ¦r Algebra - bennike.org

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