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 $\mathbf{u}$ 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 $a\mathbf{u}=\mathbf{0}$ 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