{"product_id":"linear-algebras-paperback-9781107493940","title":"Linear Algebras (Paperback \/ softback) 9781107493940","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eLinear Algebras\u003c\/font\u003e\u003cbr\u003e\r\n\r\n\r\n\u003c\/p\u003e\n\u003cp\u003e\u003cem\u003eOriginally published in 1914, this book provides a concise account regarding the theory of linear associative algebras.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eL. E. Dickson (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9781107493940, Cambridge University Press\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePaperback \/ softback, published 26 March 2015\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e82 pages\u003cbr\u003e22 x 14 x 1 cm, 0.12 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003eOriginally published in 1914 as number sixteen in the Cambridge Tracts in Mathematics and Mathematical Physics series, this book provides a concise account regarding the theory of linear associative algebras. Textual notes are incorporated throughout. This book will be of value to anyone with an interest in algebra and the history of mathematics.\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003ePreface\u003cbr\u003e Part I. Definitions, Illustrations and Elementary Theorems: 1-2. Ordinary complex numbers, number fields\u003cbr\u003e 3-4. Matrices\u003cbr\u003e matric algebra as a linear algebra\u003cbr\u003e 5. Definition of linear algebras, coordinates, units\u003cbr\u003e 6-8. Division\u003cbr\u003e principal unit\u003cbr\u003e transformation of units\u003cbr\u003e 9-10. Equations and polynomials in a single number\u003cbr\u003e 11. Unique place of quaternions among algebras\u003cbr\u003e 12-13. Properties of quaternions, relation to matrices\u003cbr\u003e 14. Cayley's generalization of real quaternions\u003cbr\u003e 15-17. Characteristic determinanats\u003cbr\u003e invariance\u003cbr\u003e 18. Binary algebras\u003cbr\u003e 19. Rank and rank equations of an algebra\u003cbr\u003e 20. Ternary algebras with a modulus\u003cbr\u003e 21-22. Reducibility, direct sum, direct product\u003cbr\u003e 23-24. Units normalized relative to a number\u003cbr\u003e example\u003cbr\u003e Part II. Revision of Cartan's General Theory of Complex Linear Associative Algebras with a Modulus: 25-27. Units having a character\u003cbr\u003e example\u003cbr\u003e 28-34. Nilpotent numbers, normalized units\u003cbr\u003e examples\u003cbr\u003e 35. Separation of algebras into two categories\u003cbr\u003e 36-38. Algebras A1 of first category, nilpotent algebras\u003cbr\u003e 39. Normalized units for A1\u003cbr\u003e 40-45. Algebras A2 of the second category\u003cbr\u003e 46. Any A2 has a quaternion sub-algebra\u003cbr\u003e 47-48. Normalized units for A2\u003cbr\u003e determinant\u003cbr\u003e 49. Invariant sub-algebra, simple algebras\u003cbr\u003e 50-51. Main theorem\u003cbr\u003e commutative case\u003cbr\u003e Part III. Relations of Linear Algebras to Other Subjects: 52. Linear associative algebras and linear groups\u003cbr\u003e 53. Linear associative algebras and bilinear forms\u003cbr\u003e 54. Relations of linear algebras and finite groups\u003cbr\u003e 55. Dedekind's view for commutative associative algebras\u003cbr\u003e Part IV. Linear Algebras over a Field F: 56. Statement of main theorem\u003cbr\u003e real simple algebras\u003cbr\u003e 57. Algebras of Weierstrass\u003cbr\u003e 58-60. Division algebras\u003cbr\u003e 61. Statement of further results\u003cbr\u003e 62. Analytic functions of hypercomplex numbers.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: History of engineering \u0026amp; technology [\u003ca title=\"See our other books on History of engineering \u0026amp; technology\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22History%20of%20engineering%20\u0026amp;%20technology%20%5BTBX%5D%22\"\u003eTBX\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Cambridge University Press","offers":[{"title":"Default Title","offer_id":46265752355096,"sku":"9781107493940","price":19.79,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/products\/9781107493940i_f7ce8788-4394-4e35-b5ff-8072ef4f9b76.jpg?v=1696754771","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/linear-algebras-paperback-9781107493940","provider":"Freshly Printed Books","version":"1.0","type":"link"}