Ruang vektor

Dalam matematik, fizik dan kejuruteraan, ruang vektor (juga dipanggil ruang linear) ialah satu set objek yang dipanggil vektor, yang boleh ditambah bersama dan didarabkan ("berskala") dengan nombor yang dipanggil skalar. Skalar selalunya ialah nombor nyata, tetapi sesetengah ruang vektor mempunyai pendaraban skalar dengan nombor kompleks atau, secara amnya, dengan skalar daripada sebarang medan matematik. Operasi penambahan vektor dan pendaraban skalar mesti memenuhi keperluan tertentu, dipanggil aksiom vektor. Untuk menentukan sama ada skalar dalam ruang vektor tertentu ialah nombor nyata atau nombor kompleks, istilah ruang vektor nyata dan ruang vektor kompleks sering digunakan.[1][2]

Penambahan vektor dan pendaraban skalar: vektor v (biru) ditambah kepada vektor w (merah, ilustrasi atas). Di bawah, w diregangkan dengan faktor 2, menghasilkan hasil tambah v + 2w.

Catatan
  1. "5: Vector Spaces". Mathematics LibreTexts (dalam bahasa Inggeris). 2016-02-29. Dicapai pada 2020-08-23.
  2. Weisstein, Eric W. "Vector Space". mathworld.wolfram.com (dalam bahasa Inggeris). Dicapai pada 2020-08-23.

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