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A Treatise on the Theory of Determinants
A Treatise on the Theory of Determinants
Date: 15 April 2011, 18:18

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One of the few comprehensive single-volume treatments of determinants, this compilation features nearly all of the known facts about determinants up to the early 1930s. The text explores permutations and combinations; general principles of simple determinants; compound determinants; co-factors; adjugates; rectangular arrays and matrices; linear dependence; more. Includes 485 problems, plus numerous examples. 1933 edition.
Contents
Chapter I.
Section I. Permutations 1
Section II. Combinations 7
Chapter II. Definitions and Notations 13
Chapter III. General Properties 23
Chapter IV. Minors and Expansions 53
Chapter V. Multiplication 138
Chapter VI. Compound Determinants 165
Chapter VII. Rectangular Arrays 213
Chapter VIII. Elimination 258
Chapter IX. Bipartites 295
Chapter X. Aggregates 313
Chapter XI. Alternants 321
Chapter XII. Symmetric Determinants 364
Section I. Centrosymmetric 364
Skew-Centrosymmetric 368
Section II. Axisymmetric 368
Zero-Axial Skew 392
Skew 410
Persymmetric 419
Circulants 442
Block Circulants 485
Section III. Aggregates 494
Chapter XIII. Continuants 516
Chapter XIV. Orthogonants 566
Chapter XV. Determinantal Equations 603
Chapter XVI. Jacobians 635
Chapter XVII. Hessians 654
Chapter XVIII.Wronskians 662
Chapter XIX. Bordered Determinants 673
Chapter XX. Determinants whose elements are combinatory numbers 679
Chapter XXI. Recurrents 700
Chapter XXII. Invariant Factors 734
Chapter XXIII.Multilineants 742
Chapter XXIV. Determinants of Higher Class 745
Chapter XXV. Less common Forms 757

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