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evilpostingmong
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Homework Statement
Prove that if eigenvectors v1, v2...vn are such that for any eigenvalue c
of A, the subset of all these eigenvectors belonging to c is linearly independent,
then the vectors v1,v2..vn are linearly independent.
Homework Equations
The Attempt at a Solution
One question: How does the fact that a subset is linearly independent
prove that every vector is linearly independent? For example:
if {v1...vi} is linearly independent, i<n but {v1...vn} is not,
then obviously the entire set is not linearly independent, though the
subset is.