The matrix determinant is an important branch of matrix analysis.By using the matrix outer algebra,the cal-culation of the determinant can be converted into the trace of the matrix.In this paper,firstly,an equivalent form of Ky Fan theorem is given,then Ky Fan theorem can be obtained by using Brunn-Minkowski inequality.Secondly,a generalization of Ky Fan theorem also can be obtained by using the properties of convex functions.
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