solve for X for each eig. value: (A-(eig. val.)I)X=0
Hi I am attempting to determine the eigenvalues and eigenvectors of a 2x2 matrix.
So how to do the following Matlab instruction "manually":
>> A = [1 1; 1 2]
A =
1 1
1 2
>> [V, D] = eig(A)
V =
-0.8507 0.5257
0.5257 0.8507
D =
0.3820 0
0 2.6180
>>
I already managed to determine the diagonal matrix D with the eigenvalues but
how can I get the matrix v that contains the eigenvectors?
so by inserting 0.38 into the equation I get:
0.62x1 + x2 = 0
x1 + 1.62x2 = 0
sorry for the stupid question but
while trying to solve this I cannot get one of the already determined eigenvectors using MatLab?
no the problem is:
it's all zero
0.62x1 + x2 = 0 (I)
x1 + 1.62x2 = 0 (II)
by extending (I) with 0.62^-1 I get
x1 + 1.62x2 = 0
so (II) - (I) is zero at all !!! so how to
get
-0.8507 0.5257
0.5257 0.8507 ??
hmmh sorry but how to get such a vector out of:
0.62x1 + x2 = 0 it's an equation with 2 unkown components x1 and x2
where is the trick I don't take into account until now?
So what brings me from 0.62x1 + x2 = 0
to V = -0.8507 0.5257 0.5257 0.8508 ?
ok i already realized there is a connection between these values
but why did MatLab chose -0.8507 0.5257 it seems to be normalized to 1 sqrt(x1^2 +x2^2)?
why can't I just say hej k= is -1 and so
the vector would be [-1 0.62]????