Thread: Finding the eigenvector

Given a specific Eigenvalue , how do I find an eigenvector of a Matrix ?

Specifically, if and

By the way, is there a way to make my Matrix look a little neater/lined up?

If is an eigenvector, then

There will be infinitely many eigenvectors corresponding the the eigenvalue 4, so just pick one of them.

Originally Posted by Nerdfighter

By the way, is there a way to make my Matrix look a little neater/lined up?

Instead of centre-aligning them, right-align them (as I have done).

How Do I pick one? I obviously can't pick any numbers for x, y, and z.

I did not say pick any numbers for Pick so that they satisfy the eigenvalue equation.

Originally Posted by TheAbstractionist

I did not say pick any numbers for Pick so that they satisfy the eigenvalue equation.

What is a good method to find such that satisfies the eigenvalue equation?

Could I simply pick the zero vector to be an eigenvector?

Originally Posted by Nerdfighter

Given a specific Eigenvalue , how do I find an eigenvector of a Matrix ?

Specifically, if and

By the way, is there a way to make my Matrix look a little neater/lined up?

Solve the matrix equation



Since your eigen value is 4 we get







putting this in reduced row form we get



Solving the above homogenious equation gives

or



So that is the eigen vector

p.s if you use the \begin{bmatrix} \end{bmatrix} tags it will auto format all of your columns

Thank you, that's what I needed!

Originally Posted by Nerdfighter

Could I simply pick the zero vector to be an eigenvector?

No, the zero vector is never an Eigenvector, as if it was every scalar would be an Eigenvalue. An Eigenvector for the corresponding Eigenvalue is defined to be a "non-zero vector such that ".

Originally Posted by Swlabr

No, the zero vector is never an Eigenvector, as if it was every scalar would be an Eigenvalue. An Eigenvector for the corresponding Eigenvalue is defined to be a "non-zero vector such that ".

Ooh, very good to know. Thank you.