non-zero vector

A non-zero vector in a vector space $V$ is a vector that is not equal to the zero vector in $V$.

If $𝐮$ is a non-zero vector in $V$ and $a$ is a scalar, i.e. an element of the field over which $V$ is defined, then the equation  $a𝐮=\mathrm{𝟎}$  is possible only in the case  $a=0$.

Title	non-zero vector
Canonical name	NonzeroVector
Date of creation	2013-12-01 16:50:29
Last modified on	2013-12-01 16:50:29
Owner	matte (1858)
Last modified by	pahio (2872)
Numerical id	6
Author	matte (2872)
Entry type	Definition
Classification	msc 15-00