http://sites.science.oregonstate.edu/coursewikis/GO/ 2020-01-26T13:07:54-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/ http://sites.science.oregonstate.edu/coursewikis/GO/lib/images/favicon.ico text/html 2014-04-07T16:42:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/22non?rev=1396914120 The $2\times2$ Eigenvalue Problem with Non-Real Eigenvalues text/html 2014-04-07T16:42:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/22real?rev=1396914120 The $2\times2$ Eigenvalue Problem with Real Eigenvalues text/html 2014-08-13T17:40:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/2square?rev=1407976800 The $2\times2$ Magic Square text/html 2014-04-07T16:42:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/33non?rev=1396914120 The $3\times3$ Eigenvalue Problem with Non-Real Eigenvalues text/html 2014-04-07T16:42:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/33real?rev=1396914120 The $3\times3$ Eigenvalue Problem with Real Eigenvalues text/html 2014-09-04T11:26:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/3psi?rev=1409855160 The $3$-$\Psi$ Rule text/html 2014-08-13T17:40:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/3square?rev=1407976800 The $3\times3$ Magic Square text/html 2014-07-05T13:58:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/aa?rev=1404593880 The Albert Algebra text/html 2012-04-08T12:35:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/acknowledge?rev=1333913700 Acknowledgments text/html 2012-07-10T20:06:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/calg?rev=1341975960 Algebra text/html 2014-09-03T17:57:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/cayley?rev=1409792220 Cayley Spinors text/html 2012-07-10T20:15:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/cd?rev=1341976500 The Cayley-Dickson Process text/html 2012-07-10T20:07:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/cgeom?rev=1341976020 Geometry text/html 2014-08-13T17:32:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/ch1?rev=1407976320 Preface Acknowledgments Chapter 1: Introduction * (ss)1. Introduction Part I: Number Systems Chapter 2: The Geometry of the Complex Numbers Chapter 3: The Geometry of the Quaternions Chapter 4: The Geometry of the Octonions Chapter 5: Other Number Systems text/html 2014-08-13T17:31:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/ch10?rev=1407976260 Preface Acknowledgments Chapter 1: Introduction Part I: Number Systems Chapter 2: The Geometry of the Complex Numbers Chapter 3: The Geometry of the Quaternions Chapter 4: The Geometry of the Octonions Chapter 5: Other Number Systems Part II: Symmetry Groups Chapter 6: Some Orthogonal Groups text/html 2014-07-03T10:50:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/ch10float?rev=1404409800 (ss)1. Lie Groups (ss)2. Lie Algebras (ss)3. Classification (ss)4. Real Forms text/html 2014-08-13T17:31:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/ch11?rev=1407976260 Preface Acknowledgments Chapter 1: Introduction Part I: Number Systems Chapter 2: The Geometry of the Complex Numbers Chapter 3: The Geometry of the Quaternions Chapter 4: The Geometry of the Octonions Chapter 5: Other Number Systems Part II: Symmetry Groups Chapter 6: Some Orthogonal Groups text/html 2014-07-07T12:19:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/ch11float?rev=1404760740 (ss)1. The Geometry of $G_2$ (ss)2. The Albert Algebra (ss)3. The Geometry of $F_4$ (ss)4. The Geometry of $E_6$ (ss)5. The Geometry of $E_7$ (ss)6. The Geometry of $E_8$ text/html 2014-08-21T12:43:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/ch12?rev=1408650180 Preface Acknowledgments Chapter 1: Introduction Part I: Number Systems Chapter 2: The Geometry of the Complex Numbers Chapter 3: The Geometry of the Quaternions Chapter 4: The Geometry of the Octonions Chapter 5: Other Number Systems Part II: Symmetry Groups Chapter 6: Some Orthogonal Groups text/html 2014-08-21T12:43:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/ch12float?rev=1408650180 (ss)1. The Hopf Bundles (ss)2. Projective Lines (ss)3. Spinors (ss)4. Möbius Transformations (ss)5. Projective Planes (ss)6. Quaternionic Integers (ss)7. Octonionic Integers (ss)8. The $\ee_8$ Lattice text/html 2014-09-03T17:21:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/ch13?rev=1409790060 Preface Acknowledgments Chapter 1: Introduction Part I: Number Systems Chapter 2: The Geometry of the Complex Numbers Chapter 3: The Geometry of the Quaternions Chapter 4: The Geometry of the Octonions Chapter 5: Other Number Systems Part II: Symmetry Groups Chapter 6: Some Orthogonal Groups text/html 2014-09-03T17:22:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/ch13float?rev=1409790120 (ss)1. Hermitian Matrices (ss)2. $2\times2$: Real Eigenvalues (ss)3. $2\times2$: Non-Real Eigenvalues (ss)4. $3\times3$: Real Eigenvalues (ss)5. $3\times3$: Non-Real Eigenvalues (ss)6. Jordan Eigenvalue Problem (ss)7. Diagonalizing Jordan Matrices text/html 2014-09-04T11:25:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/ch14?rev=1409855100 Preface Acknowledgments Chapter 1: Introduction Part I: Number Systems Chapter 2: The Geometry of the Complex Numbers Chapter 3: The Geometry of the Quaternions Chapter 4: The Geometry of the Octonions Chapter 5: Other Number Systems Part II: Symmetry Groups Chapter 6: Some Orthogonal Groups text/html 2014-09-04T11:25:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/ch14float?rev=1409855100 (ss)1. Spin (ss)2. Quaternionic Spin (ss)3. Intro to Dirac Equation (ss)4. Gamma Matrices (ss)5. The Dirac Equation (ss)6. The Weyl Equation (ss)7. Leptons (ss)8. Cayley Spinors (ss)9. Jordan QM (ss)10. The $3$-$\Psi$ Rule text/html 2014-09-01T22:08:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/ch15?rev=1409634480 Preface Acknowledgments Chapter 1: Introduction Part I: Number Systems Chapter 2: The Geometry of the Complex Numbers Chapter 3: The Geometry of the Quaternions Chapter 4: The Geometry of the Octonions Chapter 5: Other Number Systems Part II: Symmetry Groups Chapter 6: Some Orthogonal Groups text/html 2014-09-01T22:07:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/ch15float?rev=1409634420 (ss)1. $2\times2$ Magic Square (ss)2. $SU(2,\KK'\otimes\KK)$ (ss)3. $3\times3$ Magic Square text/html 2012-07-10T23:20:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/ch16?rev=1341987600 Preface Acknowledgments Chapter 1: Introduction Part I: Number Systems Chapter 2: The Geometry of the Complex Numbers Chapter 3: The Geometry of the Quaternions Chapter 4: The Geometry of the Octonions Chapter 5: Other Number Systems Part II: Symmetry Groups Chapter 6: Some Orthogonal Groups text/html 2012-07-10T23:20:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/ch16float?rev=1341987600 text/html 2012-07-10T23:29:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/ch1float?rev=1341988140 text/html 2014-08-13T17:32:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/ch2?rev=1407976320 Preface Acknowledgments Chapter 1: Introduction Part I: Number Systems Chapter 2: The Geometry of the Complex Numbers * (ss)1. Introduction * (ss)2. History * (ss)3. Algebra * (ss)4. Geometry Chapter 3: The Geometry of the Quaternions text/html 2014-03-28T09:17:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/ch2float?rev=1396023420 (ss)1. Introduction (ss)2. History (ss)3. Algebra (ss)4. Geometry text/html 2014-08-13T17:32:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/ch3?rev=1407976320 Preface Acknowledgments Chapter 1: Introduction Part I: Number Systems Chapter 2: The Geometry of the Complex Numbers Chapter 3: The Geometry of the Quaternions * (ss)1. Introduction * (ss)2. History * (ss)3. Algebra * (ss)4. Geometry text/html 2012-07-10T22:52:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/ch3float?rev=1341985920 (ss)1. Introduction (ss)2. History (ss)3. Algebra (ss)4. Geometry text/html 2014-08-13T17:32:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/ch4?rev=1407976320 Preface Acknowledgments Chapter 1: Introduction Part I: Number Systems Chapter 2: The Geometry of the Complex Numbers Chapter 3: The Geometry of the Quaternions Chapter 4: The Geometry of the Octonions * (ss)1. Introduction * (ss)2. History * (ss)3. Algebra * (ss)4. Geometry text/html 2012-07-10T22:53:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/ch4float?rev=1341985980 (ss)1. Introduction (ss)2. History (ss)3. Algebra (ss)4. Geometry text/html 2014-08-13T17:32:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/ch5?rev=1407976320 Preface Acknowledgments Chapter 1: Introduction Part I: Number Systems Chapter 2: The Geometry of the Complex Numbers Chapter 3: The Geometry of the Quaternions Chapter 4: The Geometry of the Octonions Chapter 5: Other Number Systems * (ss)1. The Cayley-Dickson Process * (ss)2. Sedenions * (ss)3. The Hurwitz Theorem * (ss)4. Split Complex Numbers * (ss)5. Split Quaternions * (ss)6. Split Octonions * (ss)7. Subalgebras of the Split Octonions text/html 2014-05-29T14:42:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/ch5float?rev=1401399720 (ss)1. Cayley-Dickson (ss)2. Sedenions (ss)3. The Hurwitz Theorem (ss)4. Split Complex Numbers (ss)5. Split Quaternions (ss)6. Split Octonions (ss)7. Subalgebras text/html 2014-09-05T12:10:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/ch6?rev=1409944200 Preface Acknowledgments Chapter 1: Introduction Part I: Number Systems Chapter 2: The Geometry of the Complex Numbers Chapter 3: The Geometry of the Quaternions Chapter 4: The Geometry of the Octonions Chapter 5: Other Number Systems Part II: Symmetry Groups Chapter 6: Some Orthogonal Groups * (ss)1. Rotations * (ss)2. The Geometry of $SO(2)$ * (ss)3. The Geometry of $SO(3)$ * (ss)4. The Geometry of $SO(4)$ * (ss)5. Lorentz Transformations * (ss)6. 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The Geometry of $\SU(3)$ (ss)5. The Geometry of $\SU(2,2)$ text/html 2014-08-13T17:31:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/ch8?rev=1407976260 Preface Acknowledgments Chapter 1: Introduction Part I: Number Systems Chapter 2: The Geometry of the Complex Numbers Chapter 3: The Geometry of the Quaternions Chapter 4: The Geometry of the Octonions Chapter 5: Other Number Systems Part II: Symmetry Groups Chapter 6: Some Orthogonal Groups text/html 2014-07-02T10:04:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/ch8float?rev=1404320640 (ss)1. Symplectic Transformations (ss)2. The Geometry of $Sp(4,\RR)$ (ss)3. The Geometry of $Sp(6,\RR)$ text/html 2014-09-05T12:10:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/ch9?rev=1409944200 Preface Acknowledgments Chapter 1: Introduction Part I: Number Systems Chapter 2: The Geometry of the Complex Numbers Chapter 3: The Geometry of the Quaternions Chapter 4: The Geometry of the Octonions Chapter 5: Other Number Systems Part II: Symmetry Groups Chapter 6: Some Orthogonal Groups text/html 2014-09-05T12:12:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/ch9float?rev=1409944320 (ss)1. Orthogonal Groups (ss)1.1. Quaternionic $SO(3)$ (ss)1.2. Quaternionic $SO(4)$ (ss)1.3. Octonionic $SO(7)$ (ss)1.4. Octonionic $SO(8)$ (ss)2. Unitary groups (ss)3. Lorentz groups (ss)4. Symplectic groups text/html 2012-07-10T20:06:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/chist?rev=1341975960 History text/html 2012-07-10T22:42:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/cintro?rev=1341985320 Complex Numbers text/html 2014-07-03T17:09:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/class?rev=1404432540 The Classification of Lie Algebras text/html 2012-07-10T20:16:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/csplit?rev=1341976560 Split Complex Numbers text/html 2014-09-03T17:24:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/diag?rev=1409790240 Diagonalizing Jordan Matrices using $F_4$ text/html 2014-08-13T17:41:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/dirac?rev=1407976860 Introduction to the Dirac Equation text/html 2014-04-07T16:43:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/e6?rev=1396914180 The Geometry of $E_6$ text/html 2014-04-07T16:43:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/e7?rev=1396914180 The Geometry of $E_7$ text/html 2014-04-07T16:43:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/e8?rev=1396914180 The Geometry of $E_8$ text/html 2014-08-14T21:41:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/e8latt?rev=1408077660 The Geometry of the $\ee_8$ Lattice text/html 2014-04-07T16:42:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/eigen?rev=1396914120 The Eigenvalue Problem for Hermitian Matrices text/html 2014-04-07T16:43:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/f4?rev=1396914180 The Geometry of $F_4$ text/html 2014-04-07T16:43:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/forms?rev=1396914180 Real Forms text/html 2014-04-07T16:43:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/g2?rev=1396914180 The Geometry of $G_2$ text/html 2014-08-13T17:42:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/gamma?rev=1407976920 Clifford Algebras and Gamma Matrices text/html 2014-04-07T16:43:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/hopf?rev=1396914180 The Hopf Bundles text/html 2012-07-10T20:15:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/hurwitz?rev=1341976500 The Hurwitz Theorem text/html 2012-04-08T16:04:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/intro?rev=1333926240 Introduction text/html 2014-09-03T17:55:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/jnw?rev=1409792100 The Jordan Formulation of Quantum Mechanics text/html 2014-04-07T16:42:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/jordan?rev=1396914120 The Jordan Eigenvalue Problem text/html 2014-04-07T16:41:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/leech?rev=1396914060 The Geometry 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http://sites.science.oregonstate.edu/coursewikis/GO/book/go/so2?rev=1397952120 The Geometry of $\SO(2)$ text/html 2014-06-24T17:43:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/so2k?rev=1403656980 Some Orthogonal Groups over Other Division Algebras text/html 2014-04-19T17:02:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/so3?rev=1397952120 The Geometry of $\SO(3)$ text/html 2014-04-19T17:02:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/so31?rev=1397952120 The Geometry of $\SO(3,1)$ text/html 2014-04-08T11:52:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/so3h?rev=1396983120 A Quaternionic Description of $SO(3)$ text/html 2014-04-19T17:02:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/so4?rev=1397952120 The Geometry of $\SO(4)$ text/html 2014-04-19T17:02:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/so42?rev=1397952120 The Geometry of $\SO(4,2)$ text/html 2014-04-08T11:52:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/so4h?rev=1396983120 A Quaternionic Description of $SO(4)$ text/html 2014-04-19T17:04:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/so64?rev=1397952240 The Geometry of $\SO(6,4)$ text/html 2012-07-10T22:37:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/so7?rev=1341985020 The Geometry of $SO(7)$ text/html 2014-04-08T11:49:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/so7o?rev=1396982940 An octonionic description of $SO(7)$ text/html 2012-07-10T22:37:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/so8?rev=1341985020 The Geometry of $SO(8)$ text/html 2014-04-08T11:49:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/so8o?rev=1396982940 An octonionic description of $SO(8)$ text/html 2014-07-02T10:03:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/sp2?rev=1404320580 The Geometry of $Sp(4,\RR)$ text/html 2014-06-24T17:43:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/sp2k?rev=1403656980 Some Symplectic Groups over Other Division Algebras text/html 2014-07-02T10:04:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/sp3?rev=1404320640 The Geometry of $Sp(6,\RR)$ text/html 2014-08-13T17:41:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/spin?rev=1407976860 Spin text/html 2014-04-07T16:43:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/spinors?rev=1396914180 Spinors text/html 2014-08-13T17:32:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/start?rev=1407976320 Preface Acknowledgments Chapter 1: Introduction Part I: Number Systems Chapter 2: The Geometry of the Complex Numbers Chapter 3: The Geometry of the Quaternions Chapter 4: The Geometry of the Octonions Chapter 5: Other Number Systems Part II: Symmetry Groups Chapter 6: Some Orthogonal Groups text/html 2012-07-10T22:37:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/su2?rev=1341985020 The Geometry of $SU(2)$ text/html 2012-07-10T22:36:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/su22?rev=1341984960 The Geometry of $SU(2,2)$ text/html 2014-06-24T17:43:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/su2k?rev=1403656980 Some Unitary Groups over Other Division Algebras text/html 2014-08-13T17:40:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/su2kk?rev=1407976800 The Geometry of $SU(2,\KK'\otimes\KK)$ text/html 2012-07-10T22:36:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/su3?rev=1341984960 The Geometry of $SU(3)$ text/html 2012-07-10T22:36:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/su33?rev=1341984960 The Geometry of $SU(3,3)$ text/html 2012-07-10T22:36:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/su3k?rev=1341984960 text/html 2014-08-13T17:40:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/su3kk?rev=1407976800 The Geometry of $SU(3,\KK'\otimes\KK)$ text/html 2012-07-10T22:21:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/sym?rev=1341984060 Symplectic Transformations text/html 2014-04-19T17:00:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/u1?rev=1397952000 The Geometry of $\Ug(1)$ text/html 2012-07-10T22:23:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/unitary?rev=1341984180 Unitary Transformations text/html 2014-08-13T17:42:00-08:00 http://sites.science.oregonstate.edu/coursewikis/GO/book/go/weyl?rev=1407976920 The Weyl Equation