MIT OCW 18.06 Intro to Linear Algebra 4th edt Gilbert Strang(adsbygoogle = window.adsbygoogle || []).push({});

Ch6.2 - the textbookemphasizedthat "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.

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# Matrix with repeated eigenvalues is diagonalizable...?

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