THE GAP OF THE GRAPH OF A LINEAR TRANSFORMATION

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JAVAD FAGHIH-HABIBI
RALPH HOLLINGSWORTH

Abstract




Assume that $A$ is a linear transformation from $\mathbb{C}^n$ into $\mathbb{C}^m$. The Gap of the graph of $A$ is


\[\theta(A_g)=\frac{||A||}{\sqrt{1+||A||^2}}.\]





Here $||A||$ is the operator norm of $A$. This is an extention of the result in [2], in which the first author used another  method to prove for the case of $m= n$.







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How to Cite
FAGHIH-HABIBI, J., & HOLLINGSWORTH, R. (1995). THE GAP OF THE GRAPH OF A LINEAR TRANSFORMATION. Tamkang Journal of Mathematics, 26(2), 141–143. https://doi.org/10.5556/j.tkjm.26.1995.4388
Section
Papers

References

I. Gohberg, P. Lancaster and L. Rodman., Invariant Subspaces of Matrices with Applications, John Wiley and Sons, New York, 1986.

J. F. Habibi, "The gap of the graph of a matrix," Linear Algebra Appl., 186 (1993), 55-57.