With the development of computer architecture and the introduction of cache, blocking has been the main method to optimize performance in matrix computing, and the effect of leading dimension becomes important to blocking algorithms performance.

The well-known matrix inequality (AB)~(-1)≤A~(-1)B~(-1) involving Hadamard product of positive definite matrices is refined to(AB)~(-1)≤diag((A~(-1)(α)~(-1)B(α))~(-1),(A(α′)B~(-1)(α′)~(-1))~(-1)),≤diag(A~(-1)(α)B(α)~(-1),A(α′)~(-1)B~(-1)(α′))≤A~(-1)B~(-1),where A(α) is the leading principal submatrix and α′ is the complementary sequence of α.

To express accurately the information of color distributing of an image,in this paper,two new color feature of color-based image retrieval method are proposed,which are dominant color matrix and dominant color pair matrix.