Seeking Help On Characteristic Polynomials

ArtOfSpace

Can anyone please show me how to compute for " the Characterirstic Polynomial" of a higher degree greater than 3....? Say for instance, a given 4X4 Matrix or 5X5 Matrix A.

I am fine with up to 3 degree of Polyniomial but having difficulties with order 4 or higher.... Adding to that, here is an an example with the solution, which I got out from a book. A given 4x4 Matrix A, The Charact. Polynom.., det[(1 1 2 0), (0 13 14 18), (0 -6 -6 -9), (0 -5 -6 -6)]. The Solution shown is (lamda - 1)^2 (lamda)^2.

Show me how you get to this.....as that is what I have hard times upon. Also notice, [(1 - lamda) (13 - lamda) (-6 - lamda) (-6 - lamda)] on the main diagonal of A.

Is their a much easier way, a general approach and handy to use method to computer for characteristic polynomials of higher orders...? If so, please state:- my book is just a collection of symbols and can't follow up sometimes.

I need your great help ASAP...........!

**Posted:** Mon Aug 29, 2005 1:05 am

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towersfreak2006

The characteristic polynomial for an $n$ by $n$ matrix $A$ is just $\det(A-I_n\lambda)$ . In particular, the one you seek is:
$f(\lambda) = \left| \begin{array}{cccc} 1-\lambda & 1 & 2 & 0 \\ 0 & 13-\lambda & 14 & 18\\ 0 & -...$

**Posted:** Mon Aug 29, 2005 4:59 pm

jmerry

**Posted:** Mon Aug 29, 2005 6:02 pm

ArtOfSpace

Hmmmm....I've seen something like that but stop short on tackling it. I thing I have some work to do on what you both proposed....

Thanks...,

**Posted:** Tue Aug 30, 2005 3:52 am

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