Find the extrema of a quadratic fraction for non-zero vectors

[JBNN]

I have a problem with the following linear algebra problem:

Normally, I would find a 3x3 symmetric matrix A such that [math]f(x)=x'Ax[/math]
However, I only know how to do it with "regular" linear problems like this one:


So my question is: How do you find the 3x3 symmetric matrix of the fraction in the 1st image?

 

[blamocur]

So my question is: How do you find the 3x3 symmetric matrix of the fraction in the 1st image?

You don't. Did you notice that both the numerator and denominator are homogeneous polynomials of the same power?

 

[JBNN]

You don't. Did you notice that both the numerator and denominator are homogeneous polynomials of the same power?

You're right, but is it even possible to solve the question then?

 

[blamocur]

You're right, but is it even possible to solve the question then?

Homegeneity means that the function does not change when a non-zero vector [imath](x_1,x_2,_x3[/imath] is scaled up or down. I.e., it is enough to find the extreme values on a unit sphere. Do you know how this can be done?

 

[JBNN]

Homegeneity means that the function does not change when a non-zero vector [imath](x_1,x_2,_x3[/imath] is scaled up or down. I.e., it is enough to find the extreme values on a unit sphere. Do you know how this can be done?

No I don't unfortunately

 

[Deleted member 4993]

No I don't unfortunately

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