The Perfect–Mirsky conjecture, named after Perfect and Leon Mirsky, concerns the region of the complex plane formed by the eigenvalues of doubly stochastic matrices. Perfect and Mirsky conjectured that for matrices this region is the union of regular polygons of up to sides, having the roots of unity of each degree up to as vertices. Perfect and Mirsky proved their conjecture for ; it was subsequently shown to be true for and false for , but remains open for larger values of .[SP2]
Perfect earned a master's degree through Westfield College (a constituent college for women in the University of London) in 1949, with a thesis on The Reduction of Matrices to Canonical Form.
In the 1950s, Perfect was a lecturer at University College of Swansea; she collaborated with Gordon Petersen, a visitor to Swansea at that time, on their translation of Alexandrov's book.
She completed her Ph.D. at the University of London in 1969; her dissertation was Studies in Transversal Theory with Particular Reference to Independence Structures and Graphs. She became a reader in mathematics at the University of Sheffield.
Perfect, Hazel (1963), Topics in Geometry, Pergamon, MR0155210
Perfect, Hazel (1966), Topics in Algebra, Pergamon
Bryant, Victor; Perfect, Hazel (1980), Independence Theory in Combinatorics: An introductory account with applications to graphs and transversals, London and New York: Chapman & Hall, ISBN0-412-16220-2, MR0604173
^Levick, Jeremy; Pereira, Rajesh; Kribs, David W. (2015), "The four-dimensional Perfect–Mirsky Conjecture", Proceedings of the American Mathematical Society, 143 (5): 1951–1956, doi:10.1090/S0002-9939-2014-12412-9, MR3314105