log-det 函数求导过程 

【转载：http://math.stackexchange.com/questions/38701/how-to-calculate-the-gradient-of-log-det-matrix-inverse】

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上述推导过程中使用到了矩阵逆和矩阵行列式、矩阵伴随矩阵之间的关系，如下：

【转载：http://en.wikipedia.org/wiki/Adjugate_matrix】

The adjugate of A is the transpose of the cofactor matrix C of A:

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In more detail: suppose R is a commutative ring and A is an n×n matrix with entries from R.

• The (i,j) minor of A, denoted A_ij, is the determinant of the (n − 1)×(n − 1) matrix that results from deleting row i and column j of A.

• The cofactor matrix of A is the n×n matrix C whose (i,j) entry is the (i,j) cofactor of A:

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• The adjugate of A is the transpose of C, that is, the n×n matrix whose (i,j) entry is the (j,i) cofactor of A:

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The adjugate is defined as it is so that the product of A and its adjugate yields a diagonal matrix whose diagonal entries are det(A):

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A is invertible if and only if det(A) is an invertible element of R, and in that case the equation above yields:

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