Kompendium til lineÃ¦r Algebra - bennike.org

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Kompendium til Lineæ r Algebra Politstudiet, matematik, 1. årsprøve Af Erik Bennike ⎛1 ⎞ ⎛1 ⎞ ⎛0 ⎞ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ 'D H1 + H2 = ⎜1 ⎟, H1 + H3 = ⎜0⎟ RJ H2 + 2H3 = ⎜1 ⎟ NDQ PDQ YHG DW VDPPHQOLJQH PHG ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎝0⎠ ⎝1 ⎠ ⎝2 ⎠ RSO\VQLQJHUQH L VS¡UJVPnO GLUHNWH VH DW 7 RJ 8 L YLUNHOLJKHGHQ HU EHVNULYHU GHQ VDPPH OLQH UH DIELOGQLQJ ,IOJ VS¡UJVPnO LLL InV GD VWUDNV $G LL - 51 - ⎛2 ⎜ $ = ⎜0 ⎜ ⎝4 3nVWDQGHQ HU NODUW ULJWLJ LGHW GHQ WLOK¡UHQGH PDWUL[ $ IXQGHW XQGHU L NODUW HU V\PPHWULVN MI L ¡YULJW /$ V WQ $G LLL ⎧⎛− 1⎞⎫ ⎪⎜ ⎟⎪ ⎨⎜ ⎟⎬ ⎪⎜ ⎟⎪ ⎩⎝ 1 ⎠⎭ 6HV LGHW ( − 2) = 9� VSDQ 0 -I VS¡UJVPnO 6n 9� KYLV [ ± InV DW ⎛−1⎞ ⎛−1⎞ ⎜ ⎟ ⎜ ⎟ ( ) = −2⋅ = −2⋅ ⋅⎜ 0 ⎟ = ⋅⎜ 0 � 8 [ [ W N ⎟∈9 ( − 2) 9� KYLONHW MR 9� YLVHU DW 8 ± Ž ± ⎜ 1 ⎟ ⎜ 1 ⎟ ⎝ ⎠ ⎝ ⎠ (UJR HU 9� ± LQYDULDQW XQGHU 8 ‹ (ULN %HQQLNH IHEUXDU 0 6 0 4⎞ ⎟ 0⎟ 2⎟ ⎠
Adjungeret afbildning.................... 18, 19, 21 Basis for underrum......................... 13, 23, 24 Bijektivitet ..................................... 18, 21 Billedet af et vektorsæ t .................. 16 Billedrum ....................................... 16, 17, 19 Cramers formler............................. 28 Definithed ...................................... 33, 35, 36 Determinant ................................... 26, 27, 37 Diagonalmatrix .............................. 27, 32 Dimension af underrum ................. 13, 14 Direkte sum.................................... 4, 14 Echelonmatrix................................ 8, 10 Egenrum......................................... 30 Egenvæ rdi ...................................... 30, 31, 33 Egenvæ rdimultiplicitet................... 30, 31 Gram-Schmidt ortonorm................ 14 Grassmanns dimensionssæ tn. ........ 18, 22 Grassmanns udskiftningssæ tn........ 13 Homogent ligningssystem.............. 23 Hovedunderdeterminant................. 35, 36 Hyperplan....................................... 3 Indre produkt.................................. 2 Initialettal....................................... 8, 9 Injektiv afbildning.......................... 17, 18 Invariant underrum ........................ 31 Invers matrix.................................. 10, 11 Isometri .......................................... 20 Isotrop vektor................................. 35 Karakteristisk polynomium............ 30, 31, 32 Konsistens af ligningssystemer...... 22 Koordinattransformation................ 23, 24 Kvadratisk form ............................. 34, 35 Kompendium til Lineæ r Algebra Politstudiet, matematik, 1. årsprøve Af Erik Bennike Stikordsregister: - 52 - Laplaces udviklingssæ tning ...........28 Lineæ r afbildning...........................16, 18, 21 Lineæ r (u)afhæ ngighed ..................12, 16, 17 Lineæ r relation ...............................12 Matrixmultiplikation ......................5, 6, 7 Norm af vektor ...............................2, 3 Norm af lineæ r afbildning..............19, 20 Nulrum ...........................................16, 17, 19 Operationsmatricer.........................10, 27 Ortogonal matrix............................24 Ortogonalt komplement .................15, 31 Ortonormalt vektorsæ t ...................14, 15 Ortogonalæ kvivalens......................32 Principal underdeterminant ............35,36 Rangen af en matrix .......................21, 22 Regneregler for matricer ................5, 6 Regularitet af matricer....................6, 7, 27 Rodmultiplicitet .............................31 Ræ kkeoperationer ..........................8, 10 Skalarprodukt .................................2, 34 Selvadjungeret endomorfi ..............19 Suppleringssæ t ...............................12, 13 Surjektivitet....................................17, 18 Symmetrisk afbildning...................19, 31, 32 Symmetrisk matrix.........................32, 34, 37 Søjleoperationer .............................27 Transponeret matrix .......................6, 7, 21 Udspæ nding af mæ ngde.................3, 4 Underrum .......................................3, 4, 17 Vinkel mellem vektorer..................3 Weierstrass’ determinansæ tn. ........26 Ækvivalens af ligningssystemer.....8
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Kompendium til lineÃ¦r Algebra - bennike.org

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