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

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?

Answer 1

[Torsten]

eigenvalues=solve(D==0,landa);

Best wishes

Torsten.

[Habib]

dear Torsten,

thank you for your replying, it is so useful. but is it possible to solve this equation without 'solve' function?

[Torsten]

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]

Dear Torsten,

your answers was very very useful, thanks.

best regards

habib