Nulvector

In de lineaire algebra is de nulvector van een bepaalde vectorruimte, het (unieke) neutrale element voor de optelling van vectoren. Naar de aard van de vectorruimte wordt soms een specifiekere term gebruikt, bijvoorbeeld nulfunctie.

In bijvoorbeeld het euclidisch vlak heeft de nulvector de coördinaten en in drie dimensies heeft de nulvector coördinaten (in elke basis).

In de -dimensionale euclidische ruimte wordt de nulvector gedefinieerd als

Voor alle vectoren in een vectorruimte geldt

Eigenschappen

Alle coördinaten van een nulvector zijn nul, ten opzichte van elke basis. Voor zover van toepassing is een norm en iedere kwadratische vorm van een nulvector altijd 0, en is een bilineaire afbeelding, waaronder een inproduct, van een vector met een nulvector altijd nul.

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