A treatise on the theory of determinants
Book Description
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 begins with the basic elements of permutations and combinations and sets down the notation and general principles of simple determinants, with a full discussion of such topics as row and column transformation, expansion, multiplication, minors, and symmetry. Additional topics include compound determinants, co-factors, adjugates, rectangular arrays and matrices, linear dependence, and many more subjects. Although its primary focus is upon answering reference and research needs, this book's 485 problems (plus scores of numerical examples) make it extremely useful to students and teachers.
Table Of Content
1. Permutations. Combinations.
2. Definitions and Notations.
3. General Properties.
4. Minors and Expansions.
5. Multiplication.
6. Compound Determinants.
7. Rectangular Arrays.
8. Elimination.
9. Bipartites.
10. Aggregates.
11. Alternants.
12. Symmetric Determinants.
13. Continuants.
14. Orthogonants.
15. Determinantal Equations.
16. Jacobians.
17. Hessians.
18. Wronskians.