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Mathematics
Linear and Abstract Algebra
Some questions about eigenvector computation
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[QUOTE="swampwiz, post: 5449441, member: 358750"] Well, I have been reading up, and I am getting a better idea about the theory which would answer my questions, but at present, I still am confused. Yes, I understand that the homogenous matrix EQ yields a trivial result (i.e., of all 0's), but that non-trivial results are possible when the determinant of the coefficient matrix is 0. I guess where I am confused is how to determine how many linear dependency constraints there are with such a zero-determinant matrix, since more than one dependency yields the same zero-determinant value. I have a hunch that for the eigenproblem, there is always the one linear dependency such that the eigenvectors are all relative to each other as per a certain amount, and each repeat of an eigenvalue results in another dependency. Is there any way short of doing an eigendecomposition to determine how many linear dependencies there are? Also, is the number of linear dependency constraints always equal to the difference of the matrix size and its rank? [/QUOTE]
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Mathematics
Linear and Abstract Algebra
Some questions about eigenvector computation
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