MAST20029 Engineering Mathematics, can anyone help?

[hobbitle]

Hi guys,

I'm getting myself a bit stressed out here with finding general solutions to coupled ODEs, where I end up with eigenvectors that have different signs to the answers e.g. I will get an eigenvector [1; -1] and the answers will use [-1; 1].

This is especially confusing for me when eigenvectors are complex, e.g. I will get eigenvector [cos t; -sin t] and the answers will have [-cos t; sin t].  In terms of, say, the parameterisation of a circle, these are both an anticlockwise circle but the starting points differ.  I can't figure out if this actually 'matters' in the context of finding the general solution of coupled ODEs and if it will affect the resulting phase portrait or not?

I don't THINK it should matter as multiplying an eigenvector by -1 doesn't change it's status as an eigenvector.... but I just wanted to check.

Thanks in advance.

[Hancock]

I can help you on campus sometime if you need it

[mark_alec]

You can multiple an eigenvector by any non-zero scalar and get the 'same' eigenvector.

[hobbitle]

Thanks guys yeah I think I was confusing myself over something trivial....