content_image/325748.jpg content_image/325746.jpg content_image/325745.jpg content_image/325747.jpg
following c × ( r + 1 − c ) matrix: 

Dividing the matrix into two parts, we find that 

Now consider the following matrix: 

Similarly, we have 

<img src='content_image/325748.jpg'>

<img src='content_image/325746.jpg'>

<img src='content_image/325745.jpg'>

<img src='content_image/325747.jpg'>

From the above two equations, we have N ( r + 1 , c ) = N ( r + 1 , r + 1 − c ). By induction, we obtain the lemma. 

On the other hand, it can be observed that the selection operator W in the previous subsection can be decomposed as a series of unitary row operators of type 2, type 3, and type 4, for the matrix A determines a series of type 4 unitary row operators, the matrix B determines a series of type 3 unitary row operators, and the symmetric matrix M , satisfying 

