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AuthorMac Duffee, C. C. author
TitleThe Theory of Matrices [electronic resource] / by C. C. Mac Duffee
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg, 1933
Connect tohttp://dx.doi.org/10.1007/978-3-642-99234-6
Descript V, 111 p. online resource

CONTENT

I. Matrices, Arrays and Determinants -- 1. Linear algebra -- 2. Representation by ordered sets -- 3. Total matric algebra -- 4. Diagonal and scalar matrices -- 5. Transpose. Symmetric and skew matrices -- 6. Determinants -- 7. Properties of determinants -- 8. Rank and nullity -- 9. Identities among minors -- 10. Reducibility -- 11. Arrays and determinants of higher dimension -- 12. Matrices in non-commutative systems -- II. The characteristic equation -- 13. The minimum equation -- 14. The characteristic equation -- 15. Determination of the minimum equation -- 16. Characteristic roots -- 17. Conjugate sets -- 18. Limits for the characteristic roots -- 19. Characteristic roots of unitary matrices -- III. Associated Integral Matrices -- 20. Matrices with elements in a principal ideal ring -- 21. Construction of unimodular matrices -- 22. Associated matrices -- 23. Greatest common divisors -- 24. Linear form moduls -- 25. Ideals -- IV. Equivalence -- 26. Equivalent matrices -- 27. Invariant factors and elementary divisors -- 28. Factorization of a matrix -- 29. Polynomial domains -- 30. Equivalent pairs of matrices -- 31. Automorphic transformations -- V. Congruence -- 32. Matrices with elements in a principal ideal ring -- 33. Matrices with rational integral elements -- 34. Matrices with elements in a field -- 35. Matrices in an algebraically closed field -- 36. Hermitian matrices -- 37. Automorphs -- VI. Similarity -- 38. Similar matrices -- 39. Matrices with elements in a field -- 40. Weyrโ{128}{153}s characteristic -- 41. Unitary and orthogonal equivalence -- 42. The structure of unitary and orthogonal matrices -- VII. Composition of matrices -- 43. Direct sum and direct product -- 44. Product-matrices and power-matrices -- 45. Adjugates -- VIII. Matric equations -- 46. The general linear equation -- 47. Scalar equations -- 48. The unilateral equation -- IX. Functions of Matrices -- 49. Power series in matrices -- 50. Functions of matrices -- 51. Matrices whose elements are functions of complex variables -- 52. Derivatives and integrals of matrices -- X. Matrices of infinite order -- 53. Infinite determinants -- 54. Infinite matrices -- 55. A matric algebra of infinite order -- 56. Bounded matrices -- 57. Matrices with a non-denumerable number of rows and colums


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