MIT OCW 18.06 Intro to Linear Algebra 4th edt Gilbert Strang Ch6.2 - the textbook emphasized that "matrices that have repeated eigenvalues are not diagonalizable". imgur: http://i.imgur.com/Q4pbi33.jpg and imgur: http://i.imgur.com/RSOmS2o.jpg Upon rereading...I do see the possibility to interpret this to mean that fewer than n independent eigenvectors leads to an undiagonalizable matrix...that n-all different eigenvalues ensures n-independent eigenvectors...leaving open the possibility of n-independent eigenvectors with repeated eigenvalues...? Yes, no? Because the second worked example shows a matrix with eigenvalues 1,5,5,5, and the use of diagonalization of that matrix, and Matlab is quite happy to produce a matrix of n-independent eigenvectors from this matrix. The matrix in question is 5*eye(4) - ones(4); What is the actual rule, because I don't feel clear on this.