I am working with a force measurement instrument which needs calibration via a calibration matrix. For each of a set of controlled measurements I have a vector $k$ of three known, independent values, and a corresponding vector $m$ containing three measured values, that due to instrument constraints end up being non-orthogonal.
From each measurement, I can assemble an equation in the form
$Cm = k$
where $C$ is a 3x3 calibration matrix for that measurement, found by solving the system.
My goal is to find some calibration matrix that is the least-squares best fit for ALL the measurements in the set of measurements. That would mean I would have a system like:
$Cm_1 = k_1\\ Cm_2 = k_2\\ ...\\ Cm_n = k_n$
that I would have to solve for C, and that is my question: how do I solve such a system, where I have a MATRIX as the unknown?
I am not familiar with heavy math notation, and I plan to solve this using Python (Numpy/Scipy), so I'm looking more for a theoretical basis and proper nomenclature of which kind of procedure I should use, and then I could figure out how to implement it numerically.
Any help is much appreciated, thanks for reading!