Interpret the result of eigenvecs

[sfan]

Hi, everyone

Here I am trying to find the eigenvectors of C using the function eigenvecs,

I know eigenvecs returns to all the eigenvectors of C,

My hand calculation shows the two eigenvectors corresponding to the two eigenvalues should be

[0.39;1] and [-0.64;1],

So what does [1.56;1] and [-2.56;1] represent?

Thank you very much!

Shawn

[RichardJ]

In your last expression you have a square root, which has two possible solutions (+ or -). Mathcad is showing you the two solutions.

Edit: Also see my comment about the use of the float keyword in this thread (near the end): incompatible units - PTC Community

[sfan]

Then for the eigenvectors, which pair should I use?

How to verify the ones that correspond to my hand calculation?

[RichardJ]

Well, that's the tricky thing about square roots. There is a common misconception that sqrt(x) has two solutions. It doesn't. It has two possible solutions. Absent any other information, you can only know that one of those solutions is the correct, one, but you can't know which. So what to do? One possibility is to find other information that resolves the dilemma. Another is to reformulate the problem to avoid the square root. In this particular case I'll make the observation that the way you solved for the eigenvectors by hand is not the same as the way you had Mathcad solve for them

[sfan]

Oh, that's sad...

I mean this one is pretty simple, for a 2 by 2 matrix,

but for a much complex matrix, hand calculation might not be that easy to implement.

So is there a way to avoid the use of square root?

Other method than the function eigenvecs?

[RichardJ]

So is there a way to avoid the use of square root?

Other method than the function eigenvecs?

The eigenvecs function is not the problem. It returns two values. In Mathcad you then use those values one way, and by hand you use them a different way (hint: in which I see no square roots).

Forgive me if I'm wrong, but I believe your questions are homework related. So I don't want to just give you the answer, because that's not a good way to learn.