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