# Mohr's circle and formula for eigenvectors

## Main Question or Discussion Point

Don't exist formula for the eigenvectors, all right!? Eigenvectors needs be found manually, correct!?
But and about the Mohr's circle? This physical/mathematical theory don't define clearly the direction of the eigenvectors (called principal direction) with the eigenvalues (called principal stress)?

https://en.wikipedia.org/wiki/Mohr's_circle#Mohr.27s_circle_for_a_general_three-dimensional_state_of_stresses

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jasonRF
Gold Member
Despite your four question marks, I'm not sure what you are asking here. There are certainly formulas for eigenvalues of low-dimensional (2x2,3x3 or 4x4) matrices, for example:
http://math.harvard.edu/archive/21b_fall_04/exhibits/2dmatrices/index.html
which also has formulas for eigenvectors.
There cannot be formulas for higher dimensional (>4) matrices as there does not exist formulas for the roots of polynomials of order >4.

Hopefully someone that knows something about Mohr's circle can chime in about your 3rd and 4th questions ... to me it looks like an interesting (and probably very useful) graphical technique that is used by mechanical engineers.

jason

• Bruno Tolentino
But, this article doesn't affirm nothing about the general case, when b and c are not zero...

jasonRF