How many linearly independent vectors can a eigen value have?
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As many as the dimension of the vector space!
Step-by-step explanation:
For an example, consider the identity matrix I.
Since Ix = 1x for all x, 1 is an eigenvalue for I and every vector is an eigenvector corresponding to this eigenvalue.
Consequently, a set of linearly independent eigenvectors corresponding to the eigenvalue 1 in this case, is simply any set of linearly independent vectors. In particular, any basis will do.
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