A Further Result on the Cyclic Subspace


Based on the geometric theories of vector space, a Cross-Identity theorem is proved for the relationship between the power kernels and power images of linear map on its cyclic subspace. By this result, a new approach of proof is found for the fact that a square matrix with only one eigenvalue and one-dimensional eigenspace is similar to a Jordan block matrix.

Share and Cite:

Wang, H. (2014) A Further Result on the Cyclic Subspace. Advances in Linear Algebra & Matrix Theory, 4, 96-99. doi: 10.4236/alamt.2014.42007.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Hirsch, M.W., Smale, S. and Devaney R.L. (2004) Differential Equations, Dynamical Systems, and an Introduction to Chaos. 2nd Edition, Elsevier Academic Press, San Diego.
[2] Greub, W.H. (1967) Linear Algebra. 3rd Edition, Springer, Berlin.
[3] Lancaster, P. and Tismenetsky, M. (1985) The Theory of Matrices: With Applications. Academic Press Inc., San Diego.
[4] Lang, S. (1987) Linear Algebra. 3rd Edition, Springer, New York.
[5] Axler, S. (1997) Linear Algebra Done Right. Springer, New York.
[6] Lax, P.D. (2007) Linear Algebra and Its Applications. 2nd Edition, John Wiley & Sons Inc, Hoboken, New Jersey.
[7] Roman, S. (2008) Advanced Linear Algebra. 3rd Edition, Springer, New York.
[8] Xu, Y.C. (2008) Linear Algebra and Matrix Theory. 2nd Edition, High Education Press, Beijing (in Chinese).

Copyright © 2022 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.