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The Proof and Application of Determinant Identities

Ge. Bin, Xu. XinJun

Abstract


The determinant identity of order 3 is given in this paper, which is proved by the definition of determinant. And the determinant identity of order n is proved by some elementary transformations. Under certain conditions, we apply these determinant identities to calculate some determinants and solve some linear equations. This paper not only discusses the property of determinant from a new viewpoint, but also provides a new approach to rapidly compute the determinant with letters (Symbol computation). The result can’t be obtained by the classic method, so it is a generalization of the existed results.

Keywords


Determinant, Middle block matrix, Identity, Application.

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