<![CDATA[Matrix is diagonalizable (similar with matrix diagonal) if and only if the sum of geometric multiplicities of its eigenvalues is n.If we search for an upper triangular form that is nearly diagonal as possible but is still attainable by similarity for every matrix, especially the sum of geometric multiplicities of its eigenvalues is less than n, the result is the Jordan canonical form, which is denoted by , and . In this paper, will be described how to get matrix S(in order to get matrix ) by using generalized eigenvector. In addition, it will also describe the Jordan canonical form and its properties, and some observation and application on discrete time linear system.]]>
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