The concept of "segment" and "matrix" overlapped in linguistics for a brief period, up to the late 70's when the "matrix" was buried by autosegmental phonology. The current state of the art is that "matrix" plays no role at all, and a "segment" has no formal role, though there is a way of reconstructing the concept (a "segment" is whatever is dominated by a root node). Affricates, consonant+glide sequences, and NC sequences among other things have caused all sorts of qualms about "segment" in phonology. In the historical transition to where we are, Leben's dissertation is an important first step is deconstructing the "matrix" a.k.a. segment.
In generative phonology, the "feature matrix" was taken to be what a "segment" is, mathematically speaking. In The sound pattern of English, ch. 8 section 2, Chomsky and Halle give their explication of segments, which "consist of feature columns", and which are graphically represented as a stack of features enclosed in brackets, i.e. a matrix. The main claim is that a segment is a combination of phonetic features, and they are not atomic units. In the appendix on formalism p. 391, they define "unit", "matrix" and "rule", though if you read that appendix you will understand why nobody cites it.
Various terms have been used to refer to the collection of features defining a segment: feature complex, feature bundle (originally from Bloomfield, I believe), feature matrix. In pre-autosegmental days there were two interpretations of the "matrix" in an utterance with multiple segments, such as "Buy hotdog buns". One is that there is an ordered sequence matrices, one for each segment; the other is that there is one big matrix containing an ordered series of feature-specification columns (see Clements 1985 p 226 for a small example, and Leben's dissertation sect 1.4.1). Given the full-specification assumption (that every segment has some value for every feature), these two modes of representation are interchangeable. The most popular convention was that each segment is a feature matrix.
There are two related questions about features in connection with matrices in pre-autosegmental generative phonology: are the featural elements of a segment ordered, and are they value-attribute pairs, or just values? The way matrices are typically presented in papers suggests that within the segment, there is no ordering to the features, thus [+cons,-son,-cont] is not distinct from [+cons,-cont,-son] or any of the other permutations: features are "simultaneous" within the segment; this also implies that features are pairings of name and specification. An alternative interpretation of the representation is that a segment is an ordered collection of values only, e.g. [+,-,-,+...] where value 1 refers to "consonantal", value 2 refers to "sonorant" and so on. The "matrix of unordered value-attribute pairs" can be easily translated into a "matrix of ordered values" – provided that the set of features is part of universal grammar. This was the claims for the phonetic features of SPE, but there are also diacritic features, and it was noted in SPE (fn 1 p. 390) that there is an unlimited set of diacritic features. In light of the fact that the total set of features is not fixed and varies between languages, a segment has to be interpreted as being composed of a collection of value-attribute pairs, in which case the feature specifications would be unordered (ordering would be superfluous).
Segments are obviously ordered: [æsk] is distinct from [sæk]. Under the theory where a segment is a feature matrix (unordered set of value-attribute pairs), there is ordering between matrices. It would be appropriate to mention here that there is a bit of divergence between general mathematical conventions and linguistic concepts. A segment looks like a column vector (m x 1 matrix), but the elements of a column vector are ordered. Note, though, that if diacritic features are expelled from the theory and segments are composed of a universal set of features (people basically ignored non-phonetic features), then there is considerable freedom to re-interpret representations, in terms of content and structure. A string like [æsk] could be an ordered sequence of three matrices of value-attribute pairs (the most common representation), or it could be an ordered sequence of values of the 23 features, with segments being computed from a sequence of plus and minus values in the same way that a sequence of 1s and 0s can be interpreted as a sequence of numbers in computer memory. Because the completely unstructured representation is difficult for people to parse, it was not a popular option, and graphic metaphors tend to determine theoretical interpretation -- an utterance is a sequence of matrices, where each matrix is a segment, and the content of each matrix is an unordered set of value-attribute pairs.
Now on to Leben. Leben retained most of the SPE formal system, but he added a division into two kinds of matrices. His starting point is the observation from SPE that every morpheme "falls into many categories", such as "noun"... and that "nasality" etc. is just another kind of category, where the word "inn" is a member of the categories "initial non-tense vowel", "noun" (I will interject that the former claim, that "initial non-tense vowel" is a category, is based on a bizarre epistemology). SPE did not actually have two matrices, one for morphemic features and one for segmental features, and they were unclear as to the lexical locus of non-phonetic features (e.g. are nons specified [+Noun] on every segment, the first segment, the last, can it contrast?), and indeed they had a convention spreading morphemic features to ever segment within a morpheme. Leben created the two-matrix representational theory so that "Noun, Past" etc were in "matrix two" which is one of the elements of a morpheme – and then he placed tone features in M2, for some languages. So Leben did not actually deny the segment, he factored out tone (and nasality, in Guarani) and made it be a morphemic feature, which was nevertheless converted into a semi-standard SPE segmental matrix representation. (His theory of surface contour tones was totally non-orthodox, however).