inner product

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inner product $$\cdot $% WIDTH=5 HEIGHT=4$

$\includegraphics[height=10mm]{images/innerProduct}% WIDTH=48 HEIGHT=45$

Calculates the inner product of two tensors.

The operator can be placed on the canvas in two ways:

From the Tensor Operations (``tensor'') toolbar $\resizebox{!}{2ex}{\includegraphics{images/innerProduct}}% WIDTH=15 HEIGHT=14$ ; or
By typing the letters ``innerProduct'' on the canvas and then pressing the Enter key.

It computes $\begin{displaymath} z_{i_{1},\ldots,i_{r_{x}-1},j_{1},\ldots,j_{r_{y}-1}}=\sum_{... ...1},k,i_{a+1}\ldots,i_{r_{x}-1}}y_{j_{1},\ldots,j_{r_{y}-1},k}, \end{displaymath}% WIDTH=868 HEIGHT=73$ where $a$% WIDTH=16 HEIGHT=16

is the given axis, and $$r_{x}$% WIDTH=28 HEIGHT=21$ and $$r_{y}$% WIDTH=28 HEIGHT=25$ are the ranks of $x$% WIDTH=17 HEIGHT=16

and

respectively.