Here's what the OED has to say:
I. Order of position.
1. a. Arrangement in line or ranks, esp. martial order. Phrases: in battle array, out of array (obs.).
2. A disposition of men in martial order, a display of military force. Obs.
3. The calling forth of a military force, the arming of the militia; esp. in Hist. phrase, Commission of Array.
4. concr. A host in array; a military force. Hist. The militia of a county or city.
5. Order, orderly sequence. Obs. rare.
6. a. A series of things exhibited or displayed in line or order; an imposing series.
b. Math. An arrangement of quantities or symbols in rows and columns; = MATRIX n. 6.
c. In Statistics, an arrangement of correlated phenomena or data.
d. Computing. A set of memory locations or data items in which each member is identified by a common identifier together with one or more subscripts (according to the number of dimensions of the array), so that the set can be treated as a linear series.
7. Law. The order of impanelling a jury; the panel.
II. Order of condition or state.
8. a. A condition of special preparation, or which has been attained by special preparation; the state of being specially fitted out, as for war, festivities, solemnities. Now only poet.
b. in evil array: in a bad condition, badly.
c. (Combining 6 and 8.)
9. Arrangement, order, or position of matters; a plight, a case; a (pretty) state of affairs! Obs.
10. The work of special preparation. Obs.
11. a. Outfit, attire, dress. Now only poet.
b. fig. and transf.
12. An assembly of directional radio aerials. See AERIAL a. 6b, BEAM n.1 24.
III. 13. Special Combs.: array processing, the computer processing of arrays (sense 6d); so array processor, a computer specially designed for processing arrays; spec. a specialized computer which does this, usu. by parallel processing, for a mainframe or host computer.
From I.6.a. I conclude that outside of [math.] 'Reihe' is actually okay.
I.6.b. equates 'array' with 'matrix'. This is too sloppy as the above links to Mathworld show.
Other than that, I see my points confirmed.