Timeline for Help Understanding Proof from Linear Algebra Done Right
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 22, 2014 at 18:33 | vote | accept | Scentless Apprentice | ||
| Dec 20, 2014 at 4:41 | comment | added | Scentless Apprentice | That's what I thought. Thanks! | |
| Dec 20, 2014 at 2:19 | comment | added | Nick Matteo | @ScentlessApprentice: Suppose $w$ and $v$ are eigenvectors for the eigenvalue $\lambda$, so $T w = \lambda w$ and $T v = \lambda v$. Then $T(w + v) = T w + T v = \lambda w + \lambda v = \lambda(w + v)$. | |
| Dec 19, 2014 at 23:18 | comment | added | Scentless Apprentice | Terrific explication, @Kundor. Very much appreciated. One last request for clarification. You say that "because $u_{i}$ is a linear combination of eigenvectors for $\lambda_{i}$, it is also an eigenvector for $\lambda_{i}$." This wasn't obvious to me at all. Is this because null($T - \lambda_{i}$) is a subspace of $V$? | |
| Dec 19, 2014 at 20:01 | history | answered | Nick Matteo | CC BY-SA 3.0 |