# True or False

Printable View

• April 12th 2010, 02:50 PM
nicolem1051
True or False
Two eigenvectors corresponding to the same eigenvalue must be linear dependent.
• April 12th 2010, 03:48 PM
dwsmith
I think it is true.
• April 13th 2010, 12:41 AM
HallsofIvy
No, it's false. For example, the identity matrix $\begin{bmatrix}1 & 0 \\ 0 & 1\end{bmatrix}$ has 1 as its only eigenvalue. Both [1 0] and [0 1] are eigenvectors corresponding to eigenvalue 1 and are independent.