| 1. | This type of structure is required to describe the Jordan normal form.
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| 2. | Notice that this matrix is in Jordan normal form but is not diagonal.
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| 3. | This example shows how to calculate the Jordan normal form of a given matrix.
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| 4. | While the Jordan normal form determines the minimal polynomial, the converse is not true.
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| 5. | There is a standard form for the consimilarity class, analogous to the Jordan normal form.
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| 6. | In this case " A " is similar to a matrix in Jordan normal form.
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| 7. | The Jordan Chevalley decomposition is particularly simple with respect to a basis for which the operator takes its Jordan normal form.
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| 8. | The diagonal form for diagonalizable matrices, for instance normal matrices, is a special case of the Jordan normal form.
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| 9. | The simpler triangularization result is often sufficient however, and in any case used in proving the Jordan normal form theorem.
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| 10. | In a different direction, for compact operators on a Banach space, a result analogous to the Jordan normal form holds.
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