## UNIQUENSS THEOREM OF REDUCED FORM OF THE CHARACTERISTIC MATRIX OVER A SKEW-FIELD

**Xie Bang-jie (Department of Mathematics)**

For any n-rowed Square matrix A over a Skew-fieId K, the characteristic matrix λI-A can be reduced by some elementary transformations into a diagonal form: Such that φ_1(λ)\φ_2(λ)\…\φ_s(λ), where these φ_i(λ) (i =l,2,...,s) are all monic polynomials over K.In this paper a necessary and sufficient condition that (1) is uniquely determined by A is given and the Cayley-Hamilton theorem is also generalized.

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