In an algorithm I'm working with, the same type of expression comes up multiple times:
$X = A \cdot B \cdot A'$
Where $A$ is a row-vector, $B$ is a square matrix, and then (naturally) $A'$ is a column vector, so the result $X$ is a scalar value.
Since this comes up so often, I thought the expression might have a name.
But it has been difficult to google for this, and I have no idea what it might be called.
Is there a common name for this operation to take a vector and matrix to produce a scalar?
This construction define a map $V\to\mathbb R$, where $V$ is a vector space of dimension $n$ and $B$ is a $n\times n$ matrix. That is, vectors $A$ in $V$ are transformed to the scalar is a map $$A\mapsto ABA^{\top},$$ that is dubbed quadratic form.