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## Homework Statement

Consider a symmetric (and hence diagonalizable)

*n*x

*n*matrix A. The eigenvectors of A are all linearly independant, and hence they span the eigenspace R

^{n}.

Since the matrix A is symmetric, there exists an orthonormal basis consisting of eigenvectors.

My questions are:

1) Will this orthonormal basis of eigenvectors also span the same space R

^{n}?

2) If two vectors are linearly independant, will they also be orthogornal?