How it is possible to find the eigenvalues of a 2*2 matrice without using of eigen function?

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Habib
Habib am 15 Apr. 2016
Kommentiert: Habib am 15 Apr. 2016
Hi every one,
I tried to fine eigenvalues of 2*2 A matrix with det(A-landa*I) and my script is follow as:
clc
clear all
syms landa
a=input('please enter value of a:');
b=input('please enter value of b:');
c=input('please enter value of c:');
d=input('please enter value of d:');
A=[a b; c d]; I=[1 0;0 1]; B=landa*I;
D=det(A-B)
firstly, I defined landa as syms and after finding determinant, with a=1, b=2, c=3 and d=4, the result is 'landa^2 - 5*landa - 2' . (it is a 2 degree polynomial that saved in D)
so my problem is: How I could got the coefficients of this polynomial for finding the landa1 and landa2 as eigenvalues of A matrix?

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Torsten
Torsten am 15 Apr. 2016
eigenvalues=solve(D==0,landa);
Best wishes
Torsten.
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Torsten
Torsten am 15 Apr. 2016
landa(1)=0.5*(a+d)+sqrt((0.5*(a+d))^2-(a*d-b*c));
landa(2)=0.5*(a+d)-sqrt((0.5*(a+d))^2-(a*d-b*c));
Best wishes
Torsten.
Habib
Habib am 15 Apr. 2016
Dear Torsten,
your answers was very very useful, thanks.
best regards
habib

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