✔ 最佳答案
A linear transform T: R^n --> R^n can be represented by a matrix A;
|Tx-Ty|=|Ax-Ay| =|A(x-y)|<= ||A|| |x-y|, where |*| is a norm selected in R^n, and ||*|| is the induced matrix norm for matrix of size n by n.
To see that T is Lipschitz, it suffices to show that ||A||<=k, a constant.
No matter what norm is selected in R^n[e.g. 1-norm, 2-norm, p-norm, infinite norm,...], the induced matrix norm ,defined by ||A||=sup[|x| not 0] {|Ax|/|x|}, can be shown to be finite, because of the fact that R^n is a finite dimensional space. Therefore pick k=||A|| or any larger number will do.
