- 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 n3 of S with eigenvalue equal to λ3 and a eigenvector n1 of S with eigenvalue equal to λ1. n1 and n3 are orthogonal to each other . Construct the vector v2 so that they're orthogonal to each other(n1,v2 and n3).We can prove that v2 is an eigenvector of S . But how do we prove that it corresponds to the eigenvalue λ1(λ1=λ2)?