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- Homework Statement:
- In diagonalizing a symmetric tensor S, we find that two of the eigenvalues(λ1, and λ2) are equal but the third ( λ3 ) is different. Show that any vector which is normal to n3 is then an eigenvector of S with eigenvalue equal to λ1.

- Relevant Equations:
- S n1=λ1 n1

There is a eigenvector

**n**3 of**S**with eigenvalue equal to λ3 and a eigenvector**n**1 of**S**with eigenvalue equal to λ1.**n**1 and**n**3 are orthogonal to each other . Construct the vector**v**2 so that they're orthogonal to each other(**n**1,**v**2 and**n**3).We can prove that**v**2 is an eigenvector of**S**. But how do we prove that it corresponds to the eigenvalue λ1(λ1=λ2)?