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What's the utility of the eigenvectors of a matrix?
I know that is something about quantum mechanics
I know that is something about quantum mechanics
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Originally posted by meteor
What's the utility of the eigenvectors of a matrix?
I know that is something about quantum mechanics
Originally posted by rdt2
Now think of a 3x3 matrix as representing something more complicated than a vector (it's called a tensor but that doesn't matter here). In general, the matrix will have 9 components (in 3-D), three of which are on the 'main diagonal' (top left to bottom right) and the other six of which are not. Again, there is always a coordinate system in which the 6 'off-diagonal' components are zero. In this system, the three components on the diagonal are the eigenvalues.
Originally posted by dg
This is not true! Not all matrices are diagonalizable!
A restriction to symmetric matrices would be more appropriate here as an illustration of the physical properties of eigenvalues...