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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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Start by thinking of a simple vector in 2-D. In general, it has two components. However, there is always a coordinate system in which one of the coordinates is zero (the system in which one axis is coincident with the vector).Originally posted by meteor
What's the utility of the eigenvectors of a matrix?
I know that is something about quantum mechanics
This is not true! Not all matrices are diagonalizable!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.
Point taken! I seldom have to deal with non-symmetric matrices.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...