Kunze Linear Algebra · Problem 7.3.16

Rational and Jordan Forms

Mathematics — Methods · square-root-nonsingular-matrix

Problem

Use the result of Exercise 15 to prove that if

c

is a non-zero complex number and

N

is a nilpotent complex matrix, then

(cI + N)

has a square root. Now use the Jordan form to prove that every non-singular complex

n \times n

matrix has a square root.