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Topic: similar matrices (Read 553 times) |
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MonicaMath
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similar matrices
« on: Mar 17th, 2010, 11:27am » |
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How we can prove that any 2x2 non-scalar matrices are similar if they have the same characteristic polynomial?
thankx
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Obob
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Re: similar matrices
« Reply #1 on: Mar 17th, 2010, 11:37am » |
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This follows immediately from Jordan Normal Form: either a 2x2 matrix is diagonalizable over C (i.e. similar to a diagonal matrix), or it is similar to
a 1
0 a
for some complex number a. On the other hand, the characteristic polynomial also determines the Jordan normal form, given that the matrix is non-scalar.
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