Circulant Matrices

From the "Twenty years ago, noting that the basic facts about circulant matrices and its relationship to the Discrete Fourier Transform were rediscovered over and over again, I thought it might be worthwhile to publish a small book in which these facts were summarized (1979). What I did not realize was the extent to which in the years to come circulant matrices would play a role in applications and the extent to which algebraists, numerical analysts, combinatorialists and physicists would push forward the development of generalized circulants. Such matrices are now often seen as special instances of structured or patterned matrices ... The outgrowth of the simple notion of a circulant matrix has therefore been both vast and profound. Readers who are interested in applications or generalizations of circulants beyond what is given in this volume may find a ... list of publications (and their bibliographies) to be of use." Second edition, with historical remarks and several additional references