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This question is about an equation I came across in a paper. It is more about terminology than anything else.

The paper says something like

"Consider an estimator which is a linear combination of the measurements

$\hat{x}_{k} = \sum_{i=1}^{k} A_{i} y_{i}$."

Here, $x_{k} \in \mathbb{R}^{n}$, $y_{i} \in \mathbb{R}^{m}$, and $A_{i} \in \mathbb{R}^{n \times m}$. By estimator he means $\hat{x}_{k}$ and the measurements are $y_{k}$.

However, to me, it looks more like $\hat{x}_{k}$ is a linear combination of the columns of $A_{i}$'s rather than a linear combination of $y_{i}$'s. Is the author using the term linear combinations loosely or is there some notion of linear combination where the coefficients are not scalars but matrices?

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Is your context statistical signal processing? – Manos Nov 28 '12 at 23:43
The paper is about state estimation. I think there is significant overlap between estimation and signal processing. – Mr. Fegur Nov 28 '12 at 23:47
As i mention my answer, the paper's wording is not rigorous. – Manos Nov 28 '12 at 23:51
up vote 0 down vote accepted

I believe the author of this paper uses the terminology "linear combination" loosely. Strictly speaking, your estimator is a linear combination of linear transformations of the measurements.

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