Solution Found!
Suppose T : V V is a linear transformation. Suppose T is diagonalizable (i.e., there is
Chapter 6, Problem 18(choose chapter or problem)
Suppose T : V V is a linear transformation. Suppose T is diagonalizable (i.e., there is a basis for V consisting of eigenvectors of T ). Suppose, moreover, that there is a subspace W V with the property that T (W) W. Prove that there is a basis for W consisting of eigenvectors of T . (Hint: Using Exercise 3.4.17, concoct a basis for V by starting with a basis for W. Consider the matrix for T with respect to this basis. What is its characteristic polynomial?)
Questions & Answers
QUESTION:
Suppose T : V V is a linear transformation. Suppose T is diagonalizable (i.e., there is a basis for V consisting of eigenvectors of T ). Suppose, moreover, that there is a subspace W V with the property that T (W) W. Prove that there is a basis for W consisting of eigenvectors of T . (Hint: Using Exercise 3.4.17, concoct a basis for V by starting with a basis for W. Consider the matrix for T with respect to this basis. What is its characteristic polynomial?)
ANSWER:Step 1 of 2
It is given that,
Also, 
Suppose that there is a subspace 
To prove that there is a basis for 
