Characteristic Polynomials and Eigenvalues

• To: mathgroup at smc.vnet.net
• Subject: [mg19364] Characteristic Polynomials and Eigenvalues
• From: MAvalosJr at aol.com
• Date: Fri, 20 Aug 1999 23:09:40 -0400
• Sender: owner-wri-mathgroup at wolfram.com

```Gentlemen:

I have been studying linear algebra and with the aid of several programs and
add- ons to Mathematica the task has been a piece of cake. However, the time
comes when suddenly "understanding" leers its ugly head.
Given the vectors {4,-6}, {3, -7}, the characteristic polynomial is x^2 + 3 x
-10. The eigenvalues are (-5,2), the eigenvectors are (2,3) and (3,1). My
question:
What does the characteristic polynomial (since it discribes a curve) have to
do with the vectors (which are straight lines)? Or for that matter, the
eigenvalues and eigenvectors -derived from the matrix or the polynomial have
to do with the vectors?
I plotted the polynomial but can't figure out what it has to do with the
vectors.

Thanks for whatever
Manuel

```

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