adri

I got a little Algebraic problem.

In the book, they always calculate maximum and minimum for (x^T)*x=1. In that case, the maximum is the greatest eigenvalue with the eigenvector as the place of the maximum. But on previous exams, my professor asked to calculate the maximum for a constraint different than (x^T)*x=1. I found out that the maximum is always the greatest eigenvalue*a (with a from (x^T)*x=a: the constraint), but I don't know how to calculate the corresponding vector of that maximum.

So obviously, my question is: How do I calculate the vector for the maximum if the constraint isn't (x^T)*x=1?

P.S.: The problem may also be solved in the equation way: like (if I use the matrix from the example below) 4(x^2) + 4(y^2) + 4yz + 4(z^2) = 0, although it would probably make more sense to the professor if I solve it with matrices.

adri

In the book, they always calculate maximum and minimum for (x^T)*x=1. In that case, the maximum is the greatest eigenvalue with the eigenvector as the place of the maximum. But on previous exams, my professor asked to calculate the maximum for a constraint different than (x^T)*x=1. I found out that the maximum is always the greatest eigenvalue*a (with a from (x^T)*x=a: the constraint), but I don't know how to calculate the corresponding vector of that maximum.

So obviously, my question is: How do I calculate the vector for the maximum if the constraint isn't (x^T)*x=1?

P.S.: The problem may also be solved in the equation way: like (if I use the matrix from the example below) 4(x^2) + 4(y^2) + 4yz + 4(z^2) = 0, although it would probably make more sense to the professor if I solve it with matrices.

adri