Thread: Diagonalisable matrices

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How do I determine if this matrix is diagonalisable? Even with the hint im not sure, thanks..

If x is in the range of M then x is an eigenvector (with eigenvalue 1). If x is in the kernel of M then x is an eigenvector (with eigenvalue 0). Now use the "rank plus nullity = n" theorem to conclude that the matrix has lots of eigenvectors.

Originally Posted by qwerty1234

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How do I determine if this matrix is diagonalisable? Even with the hint im not sure, thanks..

Superhint: a square matrix is diagonalisable iff its minimal polynomial is the product of
different linear factors.

Tonio

...and the problem explicitly gives you the minimal polynomial of M....