Open AccessTHE GAP OF THE GRAPH OF A LINEAR TRANSFORMATION
Author(s) -
Javad Faghih-Habibi,
Ralph G. Hollingsworth
Publication year - 1995
Publication title -
tamkang journal of mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.324
H-Index - 18
eISSN - 0049-2930
pISSN - 2073-9826
DOI - 10.5556/j.tkjm.26.1995.4388
Subject(s) - mathematics , linear map , graph , combinatorics , transformation (genetics) , linear operators , norm (philosophy) , operator (biology) , discrete mathematics , pure mathematics , mathematical analysis , biochemistry , repressor , political science , transcription factor , bounded function , gene , chemistry , law
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 $m= n$.