Some outstanding problems in the theory of matrices
Charles R. Johnson · Linear and Multilinear Algebra · 1982
An informal personal survey of some major outstanding questions in matrix theory is given. These are grouped into several categories and illustrate the faci that modern work in matrix theory relies predominantly on neither linear nor algebraic techniques. Occasional references are given. Category 1 involves simultaneous conditions on sets of parameters associated with a matrix; category 2 includes restricted similarity questions, and category 3 is represented by the D-stability problem. In category 4 are questions associated with the geometry of major classes of matrices and category 5 is that of determinant optimization and inequality problems. Finallycategory 6 recognizes an area of rapidly growing interest, that of combinatorial aspects of matrix problems.