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