Kluckhohn had used it already in 1942, in Myth and Rituals: A General Theory ..., where he wrote
The structure of new cultural forms (whether myths or rituals) will undoubtedly be conditioned by the pre-existent cultural matrix. (p.52)
A more telling use occurs in his 1949 book, Mirror for Man, which uses matrix in the sense of a complete cross-product of relationships between a set of concepts.
The full significance of any single element in the culture design will be seen only when that element is viewed in the total matrix of its relationship to other elements. (p.34)
Most of these environmental influences act on each other. In the total environmental matrix now one factor, now another bears on the organism with special intensity. (p.83)
The cultural dislocation of emigrant groups, the rapid and disorderly expansion of cities, and many other factors have all contributed to the disorientation of individuals from a cohesive social matrix. (p.250)
Geertz used Kluckhohn's Mirror for Man as a negative example, criticizing the book for its plurality of definitions of what culture is, in his 1973 article on thick descriptions.
The conceptual morass into which the Tylorean kind of pot-au-feu theorizing about culture can lead, is evident in what is still one of the better general introductions to anthropology, Clyde Kluckhohn’s Mirror for Man. In some twenty-seven pages of his chapter on the concept, Kluckhohn managed to define culture in turn as: (1) “the total way of life of a people”; (2) “the social legacy the individual acquires from his group”; (3) “a way of thinking, feeling, and believing”; (4) “an abstraction from behavior”; (5) a theory on the part of the anthropologist about the way in which a group of people in fact behave; (6) a “storehouse of pooled learning”; (7) “a set of standardized orientations to re-current problems”; (8) “earned behavior”; (9) a mechanism for the normative regulation of behavior; (10) “a set of techniques for adjusting both to the external environment and to other men”; (11) “a precipitate of history”; and turning, perhaps in desperation, to similes, as a map, as a sieve, and as a matrix. In the face of this sort of theoretical diffusion, even a somewhat constricted and not entirely standard concept of culture, which is at least internally coherent and, more important, which has a definable argument to make is (as, to be fair, Kluckhohn himself keenly realized) an improvement. Eclecticism is self-defeating not because there is only one direction in which it is useful to move, but because there are so many: it is necessary to choose.[RCK: Critically, these twelve definitions are not Geertz', but Geertz' paraphrase of Kluckhohn, summarized for the purposes of criticism.] Thus, to Geertz, the use of matrix is not a proper use, but an analogical use, akin to speaking of cultural maps or sieves.
Kluckhohn continued to uses this notion in later works as well. In his 1961 book, Anthropology and the Classics, he wrote of the "intellectual matrix" of evolution (p.11).
In his Culture and Behavior: Collected Essays (1962), Kluckhohn paraphrased the total matrix definition (it is not an identical quote) and spoke of the "matrix of that [i.e. a specific, RCK] culture" in the context of contrasting cultural from universal values.
The full significance of any single element in a cultural design will be seen only when that element is viewed in the total matrix of its relationship to other elements—and indeed to other designs. (p.61)
… some values are almost purely cultural [i.e. as opposed to universal values, RCK] and draw their significance only from the matrix of that culture. (p.297)We then take the preliminary view that Kluckhohn meant something like the pairwise product of constraints of concepts upon each other, and then applied that notion successively to culture, the social, the environmental and the intellectual.