What are the Eigenvalues and Eigenvectors of a Matrix?

Jocey13

Homework Statement



Let: a matrix be: -5 -0.5
-0 -8


Find an invertible P and a diagonal D such that PDP(inverse)


Homework Equations



DET( (I)Lamda-A))= 0 for Eigenvalues

The Attempt at a Solution



when y=0 at the end matrix for finding the eigenvectors how do i make that a P
 
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what are your eigenvalues? P is a matrix whose columns will be the eigenvectors of A
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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