Phindaphinda ivekhtha ngenombolo

Kulolu shicilelo, sizocubungula ukuthi i-vector ingaphindaphindwa kanjani ngenombolo (ukutolika kwejiyomethri kanye nefomula ye-algebraic). Siphinde siklelise izici zalesi senzo futhi sihlaziye izibonelo zemisebenzi.

Okuqukethwe

Ukuchazwa kweJomethri yomsebenzi

Uma i-vector a phindaphinda ngenombolo m, bese uthola i-vector b, lapho:

  • b || a
  • |b| = |m| · |a|
  • b ↑↑ a, uma m > 0, b ↑ ↓ auma m <0

Ngakho-ke, umkhiqizo we-vector engeyona i-zero ngenombolo yi-vector:

  • i-collinear kweyokuqala;
  • i-co-directional (uma inombolo inkulu kunoziro) noma inohlangothi oluphambene (uma inombolo ingaphansi kukaziro);
  • Ubude bulingana nobude be-vector yokufaka ephindwe nge-modulus yenombolo.

Ifomula yokuphindaphinda i-vector ngenombolo

Umkhiqizo wevekhtha engeyona uziro ngenombolo iyivekhtha izixhumanisi zayo ezilingana nezixhumanisi ezihambisanayo zevekhtha yasekuqaleni, iphindwe ngenombolo enikeziwe.

Ngemisebenzi eyisicabaNgemisebenzi ye-XNUMXDOkwamavektha angu-n-dimensionalСвойства произведения вектора и числа

Для любых произвольных векторов kanye ne-чисел:

  • (m ± n) · a = m · a ± n · a
  • m · (a ± b) = m · a ± m · b
  • m · (n · a) = (m · n) · a = n · (m · a)
  • 1 · a = a
  • 0 · a = 0

Izinkinga zesampula

Umsebenzi 1

Найдем произведение вектора a = {5; 11} kanye nesiqephu 4.

Isixazululo:

4 · a = {4 · 5; 4 · 11} = {20; 44}

Umsebenzi 2

Умножим вектор b = {2; -4; 7} nge-число -6.

Isixazululo:

-6 · b = {(-6) · 2; (-6) · (-4); (-6) · 7} = {-12; 24; -42}.

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