What does eigen value and eigen vector represent in real life? Why is it so important to calculate them? Is there any practical application which will make me to understand its use?

What does eigen value and eigen vector represent in real life? Why is it so important to calculate them? Is there any practical application which will make me to understand its use?
Depends what you mean by "real life"! In the quantized version, it is assumed that any phenomenon that can be measured is the result of a linear operator acting on some vector space.
The eigenvalues for that operator represent all the possible values that this measurement may have. For more unhelpful and selfimportant gibberish you might look here
Also trying to solve systems of linear ODE's with diagonalization would be a nightmare undertaking. And guess what you need to diagonalize? Eigenvalues and Eigenvectors
This site cracks me up, it really does.
Ramanujam: You asked a question, you had two answers. In my book, you are under an obligation to post one of the following general responses:
thank you for your help, that was really helpful/confusing;
thank you, but I still don't understand why.....;
No, I don't agree, because....;
OK, but I read that .....;
or, I'm afraid you don't know what you're talking about.
Any of these would do. Silence, in these circumstances, is not a polite option!
not trying to cause trouble here, but I'd like to point out that 1. the original poster may not have returned to this thread after the new posts were made, yet, and 2. no one says anyone has to be polite. politeness isn't a given, it's a choice.
Fair points. But if I had asked a question on a board such as this, I would check for answers at least once a day. Wouldn't you?
Moreover, although you may be right that politeness is not a given, surely if people give up their time to attempt an answer to your question, an acknowledgment (at least) is in order?
Am I out of step here?
It would be nice to get decent responses guitarist, but they seem to be like hens teeth on the forum lately.
See http://www.thescienceforum.com/viewt...er=asc&start=0 for example...
Yeah, I've had dealings with this member before now. We seemed not to get along.
Anyway, maybe I should resurrect my function space thread?
Hi sramanujam,
I had the same question in the past. But now I can say that eigen values and eigen vector are not only intellectual. They represent something of palpable: for example, in quntum mechanics, we deal with "operators" (they are represented by a matrix, then they have eigen values) wich act on statefunction. The result of such action in one of the operator's eigen value.
E.g: Hψ =Eψ (Schrodinger's equation)
ψ:state function
H:the hamiltonian operator(it measures)
E: the value of energy (the result of measure)
We say H, when acting (measuring) on ψ, gives the value ( on of its eigen values ) E of energy.
I have perhaps not well explained. In fact, more concise explanation requires a long text.
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