Is the set of all 3 × 3 matrices that have the vector #[2, 1 , 2]^T# as an eigenvector closed under addition?
1 Answer
Mar 31, 2017
Yes, see below.
Explanation:
A set is closed under addition if the sum of any two elements in the set is also in the set.
Here, if 2 matrices in the set are

#M_1 mathbf e = lambda_1 mathbf e# ; and 
#M_2 mathbf e = lambda_2 mathbf e#
....where
It follows from adding these together that:
Where: