Physical significance of Eigenvalues and Eigenvector?

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1. Jul 31, 2015

kgirish

I want to know what exactly Eigen value imply. What is its Physical significance ? Physical significance of eigen vector? Does eigen value concept apply in signal processing or evalvating frequency response off a system?

2. Jul 31, 2015

Dr. Courtney

Quantum or classical? Eigen values and eigen vectors have different meanings in different contexts.

3. Jul 31, 2015

HallsofIvy

The "physical significance" of something is a physics question, not a mathematics question.

4. Jul 31, 2015

Staff: Mentor

The physical significance of an eigenvector depends on the physical significance of the matrix that it comes from.

5. Jul 31, 2015

Staff: Mentor

Eigenvalues are very useful in engineering as are differential equations and Lapace transforms, and frequency response. I'll wager you think of frequency response as something physical, but all these things are math methods that make some things easier to visualize and to manipulate.

See https://en.m.wikipedia.org/wiki/Eigenvalue,_eigenvector_and_eigenspace#Dynamic_equations to see their general usefulness to solving dynamic equations.

As DaleSpam said, the actual physical significance depends on the application, and there are many such.

If you work in signal processing someone might ask you "what is the physical significance of multiplying a signal by a transfer function?" How would you answer?