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# matrix watch

1. how do i go about knowing if a matrix e.g.
1 3
2 1

is diagonalizable over C,R,Q
2. The way I'd go about it is to find the eigenvalues and eigenvectors and go from there....do you know how to do that?
3. ye i fink so but i was told in way of using characteristic and minimum polys
ye i fink so but i was told in way of using characteristic and minimum polys
You need to use the characteristic to find the eigenvalues, so that bit seems OK...

...I think all you need to do then is to show that the characteristic polynomial has 2 distinct roots in a field F for the 2xx2 matrix to be diagonalizable over F.

In you case the fields are C, R and Q. Depending on what roots you get depends on the answer.

You can also show that the min poly is the product of linear factors over F, because this is true if and only if the matrix is diagonalizable over F.

By the looks of things you might be required to show both things...but I'd guess at the two things being fairly closely related in this example.

Hope that helps

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Updated: November 15, 2005
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