(5) A matrix A is called unipotent if A-I is nilpotent. Suppose that A E GL,(C) is an invertible nxn matrix. Prove that
Posted: Thu May 12, 2022 7:40 am
- 5 A Matrix A Is Called Unipotent If A I Is Nilpotent Suppose That A E Gl C Is An Invertible Nxn Matrix Prove That 1 (48.79 KiB) Viewed 48 times
(5) A matrix A is called unipotent if A-I is nilpotent. Suppose that A E GL,(C) is an invertible nxn matrix. Prove that there exist matrices A1, A2 E GLn(C) such that A = A1 A2 = A2A1, Aj is diagonalizable, and A2 is unipotent. (Hint: First do the case where A is in Jordan canoical form.)