some English uses of the notion of an intellectual matrix

In his 1969 postscript to the Structure of Scientific Revolution, Thomas Kuhn introduced the term disciplinary matrix (Kuhn 1970:180) as the locus of the change during the paradigm shift, and defined it as

the entire constellation of beliefs, values, techniques and so on shared by the members of a given community (Kuhn 1970:175)

In their book 2012 Objectivity and Subjectivity in Social Research, the authors Gayle Letherby, John Scott and Malcolm Williams suggested to broaden disciplinary matrix to intellectual matrix, to shed the restriction to a specific discipline or specialization (p.24 Fn 4).

In a 2013 book entitled Biblical Narrative and Palestine's History, Thomas L. Thompson of the Copenhagen School of biblical criticism used the concept of "intellectual matrix" as the basis for Chapter 8, entitled The intellectual matrix of early biblical narrative: inclusive monotheism in Persian period Palestine (pp. 105-118). This chapter repeated an argument that Thompson had published in the essay collection The Triumph of Elohim: From Yahwisms to Judaisms edited by Diana Vikander Edelman from 1995. Here, Thompson uses the terms literary matrix and intellectual matrix (pp.112-113) interchangeably to denote the interpretation of the Exile as a mental event.

Concepts and literary works commonly thought to be exilic and post exilic have referents recognized as adhering to the defining ideology of Exile — whatever the exile’s actual historicity. In such literature, the exile is presented first of all as an event of the mind within the intellectual world of early Judaism and functions as a literary matrix for large portions of the Bible. This is true whatever events, if any, actually occurred that might be regarded as a “return”. What are commonly designated as exilic and post exilic texts, as well as some of the later compose collections of the Old Testament, whether the Septuagint || or the later Massoretic [sic!] collection called the Hebrew Bible, all flow from this intellectual matrix and must, therefore, be chronologically subsequent. (pp.112-113)

Perhaps more typical of the problem is the use that James F. Ward makes in his monograph Language, Form and Inquiry: Arthur F. Bentley's Philosophy of Social Science, 1984, where the 2nd chapter is entitled The Intellectual Matrix of Bentley's Social Science, without ever defining what might be meant with that. Ward writes that:

This chapter [i.e. the 2nd chapter, RCK] is concerned with the milieu in which Bentley’s early thinking was formed and the way in which he began his course of inquiry. The central question is how Bentley arrived at the problem that unifies his work: the search for the foundations of social science. The path to the philosophy of social science led Bentley through a series of intellectual encounters which expanded the horizons of his thinking and which reveal his growing intellectual independence. (p.15)

leaving it unclear whether the intellectual matrix is understood here as the residue of the Entwicklungsroman of Bentley' intellectual encounters, or the unifying problem of Bentley's research, or something else entirely.

We owe Ellen Meiksins Wood's Citizens to Lords: A Social History of Western Political Thought (2011) the reference to and explication of Quentin Skinner's 1978 book The Foundations of Modern Political Thought, which takes a hyper-contextualizing approach to political vocabulary.

His [i.e. Quentin Skinner, RCK] main strategy, here as elsewhere in his work, was to cast his net more widely than historians of political thought have customarily done, considering not just the leading theorists but, as he put it,  “the more general social and intellectual matrix out of which their works arose”. [= Skinner, ibid, p.x] (p.8)

In Skinner's use then, the social matrix and the intellectual matrix are almost akin to levels of discourse of different parts of society, rather than agglomerations of conceptual notions.  Meiksins Wood writes:

It turns out that the ‘social matrix’ has little to do with ‘society’, the economy, or even the polity. The social context is itself intellectual, or at least the ‘social’ is defined by, and only by, existing vocabularies. The ‘political life’ that sets the || agenda for theory is essentially a language game. In the end, to contextualize a text is to situate it among other texts, among a range of vocabularies, discourses and ideological paradigms at various levels of formality, from the classics of political thought down to ephemeral screeds or political speeches. (pp.8-9)

Rob Moore, in his book Basil Bernstein: The Thinker and the Field, 2013, uses "intellectual matrix" to mean a substratum of the disciplinary or social discourse of his time.

The exegesis of [Basil, RCK] Bernstein’s thinking must involve a consideration of when he thought what he did, both in terms of the intellectual matrix of the time, the nexus of personal relationships and broader social conditions and issues. It must be concerned with the time and the place of the ideas. (p.3)

Rob Moore then equates the term ‘meta-dialogue’, coined by Hasan (1999) [= Ruqaiya Hasan, Speaking with Reference to a Context,  In M. Ghadessy (Ed.), Text and Context in Functional Linguistics: Systemic Perspectives (pp. 219-328). Amsterdam/Philadelphia: John Benjamins, 1999. RCK], as equivalent to “an intellectual matrix of ideas”, which is used to describe a 

... nexus of personal and institutional relationships — University College London (UCL), where Halliday and Douglas were based, is ‘around the corner’ from the University of London Institute of Education where Bernstein and Hasan worked. (p.15)

Jairo Moreno, in his discussion of the Argentinian Jazz musician Guillermo Klein, as part of his essay Past Identity: Guillermo Klein, Miguel Zenón, and the Future of Jazz, in: Pablo Vila (ed), Music and Youth Culture in Latin America, 2014, pp.81-105, contrasts the type of matrices which constrain Klein’s work with those that constrain, according to Lewis (2008) [= George E. Lewis, A Power Stronger Than Itself: The AACM and American Experimental Music, Chicago (University of Chicago Press), 2008. RCK], the work of African American musicians (p.88).

Moreno (p.88) quotes Lewis (2008:447) as saying that African American musicians are under an imperative to

situate their work in a complexly articulated African American intellectual, social, and sonic matrix” (Lewis 2008:447); cited (p.88)

In contrast, Moreno argues, Klein is under no such imperative; though his work is

articulated to a local-national social and intellectual matrix, and in turn to an international critical matrix that in a way preceded it and helped to shape it. What is more, these matrices rarely intersect. When they do, they disrupt as much as they enable one another. (p.88) 

Moreno interprets the notion of matrix as belonging to competing modernities.

… matrices operate independently from each other as embodiments of actually existing multiple modernities—modernities that are no longer local variants of a centrally dominant US or European modernity. (p.89) 

In 2014, S. Demazeux used the Kuhnian notion of the disciplinary matrix in an article in the International Journal of Epidemiology to analyze the consolidation of psychiatric epidemiology. Because Demazeux diagnosed a "weak coherence of its intellectual components" (Abstract), the almost-discipline is noted to have a "weak intellectual matrix" (ibid).

In his 2014 online faculty profile at Princeton, Thomas Conlan, Professor of East Asian Studies and History, uses the term the terms “social, political and intellectual matrix of fourteenth-century Japan” as the object of transformation targeted by the violence that he describes in his monograph State of War: The Violent Order of Fourteenth Century Japan (2003).

The online Encyclopedia of African-American Culture and History in its article on Intellectual Life uses the matrix terminology at least twice. For the colonial period, it denotes the shape into which the oppression of slavery confined intellectual African thinking for the slaves brought to the colonies.

... an African-American tradition of sacred and secular folk thought in sermons, tales, aphorisms, proverbs, narrative poems, sacred and secular songs, verbal games, and other linguistic forms became the primary matrix for historicizing, interpreting, and speculating about the nature and meaning of society and the cosmos.

The alternative matrix of the Enlightenment was available to the African Americans through the free schools and societies, as the article eloquently notes.

But Free African societies and fraternal orders like the Prince Hall Masons also provided a counterconventional intellectual matrix—for mastering the secular and sacred freethought traditions of the Radical Enlightenment, in which the proselytizing mythographers of freemasonry and Renaissance hermeticism offered African-American free thinkers secret access to a "perennial philosophy" that hypothesized an unbroken continuity with, and a reverential attitude toward, the esoteric symbol systems and pagan wisdom literatures of ancient North Africa and the Orient.