How to convert an equation to quadratic format

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How can I convert the following equation into quadratic format, e.g., $x^TQx$:

$\sum_{i=1}^n (\delta_i .x)^TA (\delta_i .x)$,

where $\delta_i$ is indicator function of size $T \times 1$, same size as $x$, $A$ is matrix of size $T \times T$, and $(\delta_i.x)$ is element-wise multiplication of two vectors.