References

  1. Bernau S. J., Abian A. Jordan canonical forms of matrices AB and BA. Rend. Istit. Mat. Univ. Trieste. 1989, 20(1), 101-108.
  2. Cao C. G., Tang X. M., Yang L. The Rank Conditions such that $AB$ and $BA$ are Similar and Applications. Inter. J. Algebra, 2007, 1 (6), 283-292.
  3. Flanders H. Elementary divisors of $AB$ and $BA$. Proc. Amer. Math. Soc. 1951, 2 (6), 871-874.
  4. Garcia S. R., Sherman D., Weiss G. On the similarity of AB and BA for normal and other matrices. Linear Algebra Appl. 2016, 508 (1), 14-21.
  5. Hartwig R. E. On a theorem of Flanders. Proc. Amer. Math. Soc. 1982, 85 (3), 310-312.
  6. Horn R. A., Johnson C. R. Matrix Analysis, Cambridge University Press, New York, 1985.
  7. Johnson Ch.R., Schreiner E.A. The Relationship Between $AB$ and $BA$. Amer. Math. Monthly. 103(7), (1996), 578-582.
  8. Lippert R. A., Strang G. The Jordan forms of $AB$ and $BA$. Electron. J. Linear Algebra. 2009, 18, 281-288.
  9. MacDuffee C.C. The theory of matrices, Chelsea, New York, 1946.
  10. Parker W. V. The matrices $AB$ and $BA$. Amer. Math. Monthly. 1953, 60 (5), 316-316.
  11. Parker W. V., Mitchell B.E. Elementary divisors of certain matrices. Duke Math. J. 1952, 19(3), 483-485.
  12. Prokip V.M. The structure of matrices of rank one over the domain of principal ideals with respect to similarity transformation. Math. methods and physiko-mechanical fields (in Ukrainian). 2016, 59(3), 68-76.
  13. Thompson R. C. On the matrices $AB$ and $BA$. Linear Algebra Appl. 1968, 1, 43-58.
  14. Williamson J. H. The characteristic polynomials of $AB$ and $BA$. Edinburgh Math. Notes. 1954, 39, 13-13.

Refbacks

  • There are currently no refbacks.


Creative Commons License
The journal is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported.