CHAPTER 10.12: EIGENVALUES AND
EIGENVECTORS: Theorems of eigenvalues and eigenvectors Part 5 of 6 In
this segment we are going to we are talking about some theorems about
Eigenvalues and Eigenvectors so one of
the theorems says that the eigenvectors of a symmetric matrix are orthogonal
what that basically means is that if you have a symmetric matrix the
eigenvectors which you are going to get for a for a symmetric matrix they are
going to be perpendicular to each other
they are going to be orthogonal that means the dot product of the
eigenvectors is going to be zero so if you take one eigenvector corresponding
to one eigenvalue then you find the dot product of it of the eigenvector
corresponding to another eigenvalue if it is corresponding to a symmetric
matrix which you are finding the eigenvalues of then you going to find the dot product to
be equal to zero however it does come with a fine print only if the
eigenvalues are distinct so if your eigenvalues are distinct only for those
eigenvectors you find this to be true and that’s the end of this segment. |