For what it's worth, I don't believe that metrics and matrix are related etymologically. "Metric" comes from the Greek for measuring, whereas "matrix" comes from the same word as "maternal," and the connection, AFAIK, comes from the fact that mothers would have been doing all the weaving, at the time the word developed. A "matrix" in our language can generally refer to anything with a two-dimensional sort of interweaving pattern, which would include a table where values are entered in rows and columns. It's either ironic or serendipitous that this kind of matrix can also represent a general class of transformations of objects in space (such as rotations, movements, flips, etc.) and in fact matrices can handle such transformations on any number of dimensions.

"Meter," like "matrix," is also interesting to me because of how much its meaning can stretch even in one era. "Meter" is a way of measuring distance in space, as well as rhythm in verse. The latter is particularly odd since in Elizabethan English (and maybe before?), the meter of verse can also be called "numbers"—and if you grew up as I did with The Phantom Tollboth, this terminology leads to cognitive dissonance, since words and numbers should be wholly antagonistic kingdoms. I'd love to know what sort of pre-Tollboothian sort of mind allowed those ancients to collapse the rhythms of poesy with the computations of numeracy.

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