Solution Found!
SupposeAis an n n matrix with all real entries and suppose is a complex eigenvalue of A
Chapter 7, Problem 9(choose chapter or problem)
SupposeAis an n n matrix with all real entries and suppose is a complex eigenvalue of A, with corresponding complex eigenvector v Cn. Set S = (A I)(A I). Prove that N(S) _= {0}. (Hint: Write v = x + iy, where x, y Rn.)
Questions & Answers
QUESTION:
SupposeAis an n n matrix with all real entries and suppose is a complex eigenvalue of A, with corresponding complex eigenvector v Cn. Set S = (A I)(A I). Prove that N(S) _= {0}. (Hint: Write v = x + iy, where x, y Rn.)
ANSWER:Step 1 of 2
Given that,
A is matrix with all real values. That means there is no complex elements. A does not contains the elements which are in the form of .
The characteristic equation is,
The Eigen values of matrix A are and .and which are complex values. Means they are in the form of .
Therefore,