\[\newcommand{\u}[1]{\boldsymbol{\mathsf{#1}}} \renewcommand{\b}[1]{\boldsymbol{#1}} \newcommand{\t}[1]{\textsf{#1}} \newcommand{\m}[1]{\mathbb{#1}} \def\RR{\bf R} \def\bold#1{\bf #1} \def\mbf#1{\mathbf #1} \def\uv#1{\hat{\usf {#1}}} \def\dl#1{\underline{\underline{#1}}} \newcommand{\usf}[1]{\boldsymbol{\mathsf{#1}}} \def\bs#1{\usf #1}\]

Null Tensor

Definition: Let $\boldsymbol{0}\in \mathcal{L}(\mathbb{E}^N,\mathbb{E}^N;\mathbb{R})$ be such that

\(\begin{align} \boldsymbol{0}\boldsymbol{v}=\boldsymbol{0}_{\mathbb{E}}, \end{align}\) for all \(\boldsymbol{v}\in \mathbb{E}^N\). Then $\boldsymbol{0}$ is called the null tensor.

A more general definition

Definition: The operator \(\b{0}\in \mathcal{L}(\mathbb{E}^N,\mathbb{F}^N;\mathbb{R})\) is called the null Tensor iff

\[\begin{align} \b{O}\b{v}=\b{0}_{\mathbb{F}^N}, \end{align}\]

where \(\b{v}\) is an arbitrary vector in \(\mathbb{E}^N\) and \(\b{0}_{\mathbb{F}^N}\) is the null vector in \(\mathbb{F}^N\).

[edit]