Muir T. A treatise on the theory of determinants

New York: Dover Publications; London: Constable and Company, 1960. — 793 p.When I started some years ago to make a revised edition of this text I did not anticipate that it would be such a large task and take so long a time, but the more I got into it, the more I found to do and as the object was to include pretty much all the known theorems to date, the work of covering the literature was great and indeed for one who was carrying a heavy load of teaching and administrative work it would have proven nigh impossible had not Dr. Muir’s Theory of Determinants in the Historical Order of Development been available and down so near to date.
I have tried to preserve the wording of the original test in so far as possible, but it is now forty-five years since it was published and much has been done in the field since then so there has of necessity been some change and much additional material. Several important results are imbodied among the problems and for the most part references have been intentionally omitted since the History is so available and gives every detail. The. book will undoubtedly have some imperfections, but I trust npt over many, and for any such the blame should fall upon the rev^er and not upon Dr. Muir, who has left me with a free hand.Permutations
Combinations
Definitions and Notations
General Properties
Minors and Expansions
Multiplication
Compound Determinants
Rectangular Arrays
Elimination
Bipartites
Aggregates
Alternants
Symmetric Determinants
Centrosymmetric
Skew-Centrosymmetric
Axisymmetric
Zero-Axial Skew
Skew
Persymmetric
Circulants
Block Circulants
Aggregates
Continuants
Orthogonants
Determinantal Equations
Jacobians
Hessians
Wronskians
Bordered Determinants
Determinants whose elements are combinatory numbers
Recurrents
Invariant Factors
Multilineants
Determinants of Higher Class
Less common Forms