nullityNullity2002-02-19 18:51:272006-09-23 17:10:17Definition\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\newcommand{\reals}{\mathbb{R}}
\newcommand{\natnums}{\mathbb{N}}
\newcommand{\cnums}{\mathbb{C}}
\newcommand{\lp}{\left(}
\newcommand{\rp}{\right)}
\newcommand{\lb}{\left[}
\newcommand{\rb}{\right]}
\newcommand{\supth}{^{\text{th}}}
\newtheorem{proposition}{Proposition}The \emph{nullity} of a linear mapping is the dimension of the mapping's kernel.
For a linear mapping $T:V\rightarrow W$, the nullity of $T$ gives the
number of linearly independent solutions to the equation
$$T(v)=0,\quad v\in V.$$
The nullity is zero if and only if the linear
mapping in question is injective.