Upgrade to Pro — share decks privately, control downloads, hide ads and more …

linear-algebra-in-n-minutes

hama_du
September 21, 2015

 linear-algebra-in-n-minutes

某所での勉強会の発表資料。厳密性や計算方法は彼方に放り投げた
しゃべりでの補完が多いのでスライドだけだと説明不足かも

hama_du

September 21, 2015
Tweet

More Decks by hama_du

Other Decks in Science

Transcript

  1. /෼Ͱ෼͔ͬͨؾʹͳΔ
    ઢܗ୅਺௒ೖ໳

    View Slide

  2. ͓͠ͳ͕͖
    w ߦྻͷ֓೦
    w ߦྻͷ଍͠ࢉɺఆ਺ഒɺֻ͚ࢉ
    w ߦྻͱϕΫτϧ
    w ݻ༗஋ͱݻ༗ϕΫτϧ
    w ߦྻͷ/৐

    View Slide

  3. ͜ͷࢿྉ͕Χόʔ͠ͳ͍ൣғ
    w ߦྻࣜ
    w ˠຊ౰͸ݻ༗஋ͷܭࢉʹߦྻ͕ࣜඞཁʹͳΔͷͰ͕͢ɺ࣌
    ؒͷ౎߹্ল͍͍ͯ·͢ɻ
    w /࣍ݩ ࣍ݩҎ্
    ͷઢܗม׵ʹؔ͢Δٞ࿦
    w ˠߦྻͷϥϯΫͱ͔*Nͱ͔,FSͱ͔
    w ݫີͳূ໌౳
    w ˠઢܗ୅਺ͷڭՊॻΛಡΜͰ͍ͩ͘͞ɻ

    View Slide

  4. ߦྻ





    ॎԣʹ۠੾ΒΕͨ෦԰ʹ਺ࣈ͕ฒͿ

    View Slide

  5. ͍ΖΜͳߦྻ
    B C D
    E F G
    ߦྻYߦྻ




    ߦྻYߦྻ
    B C D
    E F G
    H I J
    ߦྻYߦྻ

    View Slide

  6. ߦྻͷ଍͠ࢉ
    ଍͠ࢉ͸ɺ෦԰͝ͱͷ਺ͷ࿨
    ʢಉ͡ܗͷߦྻʹରͯ͠ఆٛ͞ΕΔʣ










    View Slide

  7. ߦྻͷఆ਺ഒ
    ఆ਺ʢεΧϥʔʣഒ͸ɺͦΕͧΕͷ෦԰ΛLഒɻ






    º

    ී௨ͷ਺

    View Slide

  8. ߦྻͱߦྻͷֻ͚ࢉ
    º






    ʁ

    View Slide

  9. ߦྻͱߦྻͷֻ͚ࢉ
    º





    Yߦྻ
    Yߦྻ

    View Slide

  10. ߦྻͱߦྻͷֻ͚ࢉ
    º





    Yߦྻ
    Yߦྻ

    View Slide

  11. ߦྻͱߦྻͷֻ͚ࢉ
    º





    Yߦྻ
    Yߦྻ

    View Slide

  12. ߦྻͱߦྻͷֻ͚ࢉ
    º





    Yߦྻ
    Yߦྻ

    View Slide

  13. ߦྻͱߦྻͷֻ͚ࢉ
    º





    Yߦྻ
    Yߦྻ

    View Slide

  14. ߦྻͱߦྻͷֻ͚ࢉ
    º





    Yߦྻ
    Yߦྻ

    View Slide

  15. ߦྻͱߦྻͷֻ͚ࢉ
    º





    Yߦྻ
    Yߦྻ

    View Slide

  16. ߦྻͱߦྻͷֻ͚ࢉ
    º





    Yߦྻ
    Yߦྻ


    View Slide

  17. ߦྻͱߦྻͷֻ͚ࢉ
    º





    Yߦྻ
    Yߦྻ


    View Slide

  18. ߦྻͱߦྻͷֻ͚ࢉ
    º





    Yߦྻ
    Yߦྻ


    View Slide

  19. ߦྻͱߦྻͷֻ͚ࢉ
    º





    Yߦྻ
    Yߦྻ


    View Slide

  20. ߦྻͱߦྻͷֻ͚ࢉ
    º





    Yߦྻ
    Yߦྻ



    View Slide

  21. ߦྻͱߦྻͷֻ͚ࢉ
    º






    View Slide

  22. ߦྻͱߦྻͷֻ͚ࢉ
    º






    View Slide

  23. ߦྻͱߦྻͷֻ͚ࢉ
    º







    View Slide

  24. ߦྻͱߦྻͷֻ͚ࢉ
    "Y#ߦྻ
    $Y%ߦྻ

    º
    #$ͷ࣌ʹͷΈఆٛ͞Εɺ݁Ռ͸ "Y%ߦྻ
    ʹͳΔ
    Ұൠʹɺ

    View Slide

  25. ϕΫτϧ






    Y
    Z
    Y
    Z
    P

    View Slide

  26. ߦྻͱϕΫτϧ




    º
    /YߦྻͱΈͳͯ͠ɺ /Y/
    /Y
    ͷֻ͚ࢉ͕Մೳ

    View Slide

  27. ߦྻͱϕΫτϧ
    ݁Ռ͸/YߦྻͱͳΓɺ
    ϕΫτϧ͕ߦྻʹΑͬͯมԽͨ͠ɺͱղऍͰ͖Δ






    º

    View Slide

  28. ߦྻͱϕΫτϧ






    º

    View Slide



  29. ߦྻͱϕΫτϧ




    º

    View Slide



  30. ߦྻͱϕΫτϧ




    º

    View Slide

  31. ߦྻͱม׵


    ˣ
    º

    View Slide

  32. ٯͷม׵













    º

    View Slide

  33. ٯߦྻͱ୯Ґߦྻ







    "" ?
    &

    View Slide

  34. ಛघͳม׵












    ٯߦྻ͸ଘࡏ͠ͳ͍


    º
    º

    View Slide

  35. ಛघͳม׵


    ٯߦྻ͸ଘࡏ͠ͳ͍
    ˣ
    º

    View Slide

  36. ͓͠ͳ͕͖
    w ߦྻͷ֓೦
    w ߦྻͷ଍͠ࢉɺఆ਺ഒɺֻ͚ࢉ
    w ߦྻͱϕΫτϧ
    w ݻ༗஋ͱݻ༗ϕΫτϧ
    w ߦྻͷ/৐

    View Slide

  37. ݻ༗஋ͱݻ༗ϕΫτϧ


    "
    #
    "
    #
    L
    ม׵ʹରͯ͠ɺେ͖͚͕ͩ͞มΘΔΑ͏ͳ
    ϕΫτϧ͕͋Δʢ৔߹͕͋Δʣ
    LΛݻ༗஋ɺɹɹɹΛݻ༗ϕΫτϧͱݺͿ
    "
    #

    View Slide

  38. ݻ༗஋ͱݻ༗ϕΫτϧ







    ʢ࣮ࡍʹ͸ɺ͜͜Ͱ঺հͨ͠ݻ༗ϕΫτϧͷఆ਺ഒ΋
    ݻ༗ϕΫτϧʹͳΔʣ







    View Slide

  39. ݻ༗ϕΫτϧͷҙຯ
    Y
    Z


    T


    U




    ͱɹɹɹɹ͸ઢܗಠཱͳͷͰ
    ͜ͷΑ͏ͳT U͸ඞͣଘࡏ͢Δ

    View Slide

  40. ݻ༗ϕΫτϧͷҙຯ
    Y
    Z


    T


    U







    T U









    Tº Uº



    View Slide

  41. ݻ༗ϕΫτϧͷҙຯ
    Y
    Z





    Tº Uº


    ΋ͱ΋ͱͷϕΫτϧ͕͍࣋ͬͯͨݻ༗ϕΫτϧͷ੒෼Λɺ
    ͦΕͧΕݻ༗஋ഒͨ͠ม׵ʹͳΔ

    View Slide

  42. ݻ༗ϕΫτϧͷҙຯ



    Y
    Z

    T
    U
    Y
    Z


    T


    U


    T
    U


    Λ୯Ґͱ͢Δ
    ੈքʹม͑Δ

    View Slide

  43. ݻ༗ϕΫτϧͷҙຯ



    Y
    Z

    T
    U





    Y
    Z

    T
    U
    ݻ༗஋ഒ͢Δ

    View Slide

  44. ݻ༗ϕΫτϧͷҙຯ





    Y
    Z

    T
    U





    Y
    Z



    Y
    Z




    Λ୯Ґͱ͢Δ
    ੈքʹ໭͢

    View Slide




  45. ݻ༗ϕΫτϧͷҙຯ







    View Slide




  46. ߦྻͷ/৐















    View Slide




  47. ߦྻͷ/৐


















    View Slide




  48. ߦྻͷ/৐
    /


    /




    View Slide

  49. B
    C

    ߦྻͷ/৐
    /
    B?/
    C?/



    /


    ?/

    ?/





    View Slide

  50. ϑΟϘφον਺ྻ
    ʜ

    View Slide

  51. ϑΟϘφον਺ྻ
    B

    B

    B O
    B O
    B O

    B O
    ΛɺOͷࣜͰද͍ͨ͠

    View Slide

  52. ϑΟϘφον਺ྻ
    ߦྻΛ͔͚ΔͱO͕ͭ૿͑Δ
    B O

    B O




    B O

    B O

    View Slide

  53. ϑΟϘφον਺ྻ
    B O

    B O




    B O

    B O



    B O

    B O




    View Slide

  54. ϑΟϘφον਺ྻ
    B O

    B O




    B

    B

    /


    /
    ͕෼͔Ε͹ɺҰൠ߲͕ग़ͤΔ

    View Slide

  55. ϑΟϘφον਺ྻ


    /
    ݻ༗஋ͱݻ༗ϕΫτϧΛग़͢͜ͱͰ/৐Ͱ͖Δ

    Ћ Ќ

    Ћ
    Ќ
    /
    Ћ Ќ


    ͨͩ͠ɺЋ Ќ͸ํఔࣜ
    Y?Y
    ͷղ

    View Slide

  56. ϑΟϘφον਺ྻ
    B O

    ܭࢉ͢Δͱ੔਺ʹͳΔ

    View Slide