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

Tensors: Motivation and Introduction.

To be more precise

Transpose of a Tensor

Definition: The transpose of a tensor \(\boldsymbol{T}\) is the tensor \(\boldsymbol{T}^{\rm T}\) that obeys the following rule

\[\begin{align} \bs{u}\cdot\left(\bs{T}\bs{v}\right)&= \bs{v}\cdot\left(\bs{T}^{\rm T}\bs{u}\right) \end{align}\]

where \(\bs{v}\) and \(\bs{u}\) are arbitrary vectors in \(\mathbb{E}^N\).

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This is the yml file