A Further Result on the Cyclic Subspace

ABSTRACT

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.

Cite this paper

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.

Wang, H. (2014) A Further Result on the Cyclic Subspace.

References

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http://dx.doi.org/10.1007/978-1-4757-1949-9

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http://dx.doi.org/10.1007/b97662

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[7] Roman, S. (2008) Advanced Linear Algebra. 3rd Edition, Springer, New York.

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[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.

http://dx.doi.org/10.1007/978-1-4757-1949-9

[5] Axler, S. (1997) Linear Algebra Done Right. Springer, New York.

http://dx.doi.org/10.1007/b97662

[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).