Matrix vs. Metric

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A matrix (plural: matrices) is a rectangle of numbers, arranged in rows and columns.

A metric or distance function is a function that defines a distance between each pair of point elements of a set.
A set with a metric is called a metric space.[1]

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In mathematics, a metric space is a set together with a metric on the set.
The metric is a function that defines a concept of distance between
any two members of the set, which are usually called points.

The metric satisfies a few simple properties. Informally:

the distance from A to B is zero if and only if A and B are the same point,
the distance between two distinct points is positive,
the distance from A to B is the same as the distance from B to A, and
the distance from A to B (directly) is less than or equal to the distance from A to B
via any third point C.