Eigenvectors corresponding to distinct eigenvalues are linearly independent. As a consequence, if all the eigenvalues of a matrix are distinct, then their corresponding eigenvectors span the space of column vectors to which the columns of the matrix belong.

How many eigenvectors are linearly independent?

Detailed Solution. There are possible infinite many eigenvectors but all those linearly dependent on each other. Hence only one linearly independent eigenvector is possible.

Why eigen vectors are linearly independent?

If A is an N × N complex matrix with N distinct eigenvalues, then any set of N corresponding eigenvectors form a basis for CN . Proof. It is sufficient to prove that the set of eigenvectors is linearly independent. ... Since each Vj = 0, any dependent subset of the {Vj} must contain at least two eigenvectors.