Review by Choice Review
Since matrices, by design, represent linear operators, one rarely encounters, as here, monographs that fall within what one might term pure matrix theory. Whereas operators dwell in some conceptual realm, matrices live right on the page in front of a reader, so the concreteness of pure matrix theory offers potential enrichment even during the early undergraduate years. Specifically, Pinkus (Technion--Israel Institute of Technology) introduces the theory of matrices possessing only nonnegative minors, i.e., all square submatrices have nonnegative determinant. Arguably, no other book covers similar territory. But a simple definition does not automatically guarantee a notion valuable to study. So while one may try to sympathize with the author's decision to keep his book short and thus omit all applications, the reader deserves at least some attempt to situate a rare topic within the larger discourse of mathematics. Further closing undergraduate readers out, the author omits proofs for the first half-dozen pages of preliminary results. These obstacles seem unfortunate, given this otherwise very readable book on an essentially elementary but important topic not treated systematically elsewhere. Unpublished notes of Mark Skandera might help as a stepping-stone before a plunge into this work. Summing Up: Recommended. Academic and professional collections, all levels. D. V. Feldman University of New Hampshire
Copyright American Library Association, used with permission.
Review by Choice Review
