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Consider the overdetermined system \begin{equation} \mathbf{A} \mathbf{X} = \mathbf{Y} \label{eq:example} \end{equation}

where $\mathbf{A}$ be a matrix of size $M \times N$, with $M > N$, $\mathbf{X}$ is a vector of size $N$ and $\mathbf{Y}$ is vector of size $M.$ I look for the proper terminology to denote "how overdetermined" the system is. If $M = 6$ and $N = 2$ it doesn't feel right writing "the system is overdetermined by a factor of $3$".

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I don't know of any established terminology to describe what you are saying.


Unless you will use it a whole lot, I also don't see any reason to introduce such a terminology since you can just say $A\in\mathbb R^{m\times n}$ where $m=3n$, for example - so new terminology wouldn't really shorten much.

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