I have two problems dealing with left eigenvectors:

(1) Show that a left eigenvectorycorrecpinding to the eigenvalue http://www.physlink.com/Images/symbols/lambda.gif of A belonging to is a right eigenvector of A* corresponding to http://www.physlink.com/Images/symbols/lambda.gif (with a bar over it).

(2) Show that ifyis a left eigenvector corresponding to the eigenvalue http://www.physlink.com/Images/symbols/lambda.gif of A belonging to theny(with a bar over it)is a right eigenvector of corresponding to http://www.physlink.com/Images/symbols/lambda.gif.

I know that the definition of left eigenvector states...the vectory≠ 0is said to be a left eigenvector of A if it satisfiesy*A = http://www.physlink.com/Images/symbols/lambda.gify*. Then http://www.physlink.com/Images/symbols/lambda.gif is called a left eigenvector of A.