- #1

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## Homework Statement

If you need to check whether an nxn matrix, A, is diagonalisable or not, do you just find out what det(XI-A) is, and then if X has n distinct values it is diagonalisable, otherwise it's not.

- Thread starter Fairy111
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- #1

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If you need to check whether an nxn matrix, A, is diagonalisable or not, do you just find out what det(XI-A) is, and then if X has n distinct values it is diagonalisable, otherwise it's not.

- #2

matt grime

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Consider the identity matrix...

- #3

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The identity matrix has only one distinct solution, 1, but it is diagonalisable...

So how do you go about checking whether or not a matrix is diagonalisable or not?

- #4

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A nxn square matrix is diagonizable if it has n linearly independent eigenvectors. Having n distinct eigenvalues is sufficient but not necessary for diagonalizability.

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