"Let $A$ be a $5\times 5$ random matrix and let $B = A^TA$ (note that the entries of the matrix $B$ are symmetric with respect to the diagonal. Such a matrix is called a symmetric matrix). Find a basis of eigenvectors for the matrix $B$, and check that this basis is orthogonal."
Does anyone know how to do this, especially in Matlab? I am only really familiar with how to find eigenvalues.