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.