Matritsa haqida Matritsaviy eksponenta

Adabiyotlar :

1. 
    Hall 2015 Equation 2.1
   
2. 
    Hall 2015 Proposition 2.3
   
3. 
    Hall 2015 Theorem 2.12
   
4. 
    Hall 2015 Theorem 2.11
   
5. 
    Hall 2015 Chapter 5
   
6. 
    Bhatia, R. (1997). Matrix Analysis. Matematikadan aspirantura matnlari. 169. Springer. ISBN 978-0-387-94846-1.
   
7. 
    E. H. Lieb (1973). "Convex trace functions and the Wigner–Yanase–Dyson conjecture". Matematikaning yutuqlari. 11 (3): 267–288. doi:10.1016/0001-8708(73)90011-X.
   
8. 
    H. Epstein (1973). "Remarks on two theorems of E. Lieb". Matematik fizikadagi aloqalar. 31 (4): 317–325. Bibcode:1973CMaPh..31..317E. doi:10.1007/BF01646492. S2CID 120096681.
   
9. 
    Hall 2015 Exercises 2.9 and 2.10
   
10. 
     R. M. Wilcox (1967). "Exponential Operators and Parameter Differentiation in Quantum Physics". Matematik fizika jurnali. 8 (4): 962–982. Bibcode:1967JMP.....8..962W. doi:10.1063/1.1705306.
    
11. 
     Hall 2015 Theorem 5.4
    
12. 
     "Matrix exponential – MATLAB expm – MathWorks Deutschland". Mathworks.de. 2011-04-30. Olingan 2013-06-05.
    
13. 
     "GNU Octave – Functions of a Matrix". Network-theory.co.uk. 2007-01-11. Arxivlandi asl nusxasi 2015-05-29. Olingan 2013-06-05.
    
14. 
     "scipy.linalg.expm function documentation". The SciPy Community. 2015-01-18. Olingan 2015-05-29.
    
15. 
     Qarang Hall 2015 Section 2.2
    
16. 
     in a Euclidean space
    
17. 
     Weyl, Hermann (1952). Space Time Matter. Dover. p. 142. ISBN 978-0-486-60267-7.
    
18. 
     Bjorken, James D.; Drell, Sidney D. (1964). Relativistic Quantum Mechanics. McGraw-Hill. p.22.
    
19. 
     Rinehart, R. F. (1955). "The equivalence of definitions of a matric function". Amerika matematikasi oyligi, 62 (6), 395-414.
    
20. 
     This can be generalized; in general, the exponential of J_n(a) is an upper triangular matrix with e^a/0! on the main diagonal, e^a/1! on the one above, e^a/2! on the next one, and so on.
    
21. 
     Ignacio Barradas and Joel E. Cohen (1994). "Iterated Exponentiation, Matrix-Matrix Exponentiation, and Entropy" (PDF). Academic Press, Inc. Archived from asl nusxasi (PDF) on 2009-06-26.
    

• 
  Hall, Brian C. (2015), Lie groups, Lie algebras, and representations: An elementary introduction, Matematikadan magistrlik matnlari, 222 (2nd ed.), Springer, ISBN 978-3-319-13466-6
  
• 
  Horn, Roger A.; Johnson, Charles R. (1991). Topics in Matrix Analysis. Kembrij universiteti matbuoti. ISBN 978-0-521-46713-1..
  
• 
  Moler, Cleve; Van Loan, Charles F. (2003). "Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later" (PDF). SIAM sharhi. 
  
• 
  45 (1): 3–49. Bibcode:2003SIAMR..45....3M. CiteSeerX 10.1.1.129.9283. doi:10.1137/S00361445024180. ISSN 1095-7200..
  
• 
  Suzuki, Masuo (1985). "Decomposition formulas of exponential operators and Lie exponentials with some applications to quantum mechanics and statistical physics". Matematik fizika jurnali. 26 (4): 601–612. Bibcode:1985JMP....26..601S. doi:10.1063/1.526596.
  
• 
  Curtright, T L; Fairlie, D B; Zachos, C K (2014). "A compact formula for rotations as spin matrix polynomials". Symmetry, Integrability and Geometry: Methods and Applications. 10: 084. arXiv:1402.3541. Bibcode:2014SIGMA..10..084C. doi:10.3842/SIGMA.2014.084. S2CID 18776942.
  
• 
  Householder, Alston S. (2006). The Theory of Matrices in Numerical Analysis. Dover Books on Mathematics. ISBN 978-0-486-44972-2.
  
• 
  Van Kortryk, T. S. (2016). "Matrix exponentials, SU(N) group elements, and real polynomial roots". Matematik fizika jurnali. 57 (2): 021701. arXiv:1508.05859. Bibcode:2016JMP....57b1701V. doi:10.1063/1.4938418. S2CID 119647937.