alpha]] denotes the

principal submatrix determined by the rows and columns indexed by [alpha].

k], the leading

principal submatrix of order k of H.

q]) has a leading

principal submatrix of type [mu] where [mu] [?

Zhang, Least squares solutions to AX = B for bisymmetric matrices under a central

principal submatrix constraint and the optimal approximation, Numer.

v](G) be the

principal submatrix of L(G) obtained by deleting the row and column corresponding to the vertex v.

For example, Deift and Nanda [4] discussed an inverse eigenvalue problem of a tridiagonal matrix under a submatrix constraint; Peng and Hu [16] considered an inverse eigenpair problem of a Jacobi matrix under a leading

principal submatrix constraint; Peng and Hu [17] studied a inverse problem of bi-symmetric matrices with a leading

principal submatrix constraint, for more we refer the reader to [6, 12, 24].

2] = C, we refer to the matrix A(C, C) = A(C) as the

principal submatrix of A on C.

Proof: Let Z be the

principal submatrix of the matrix Z (54) corresponding to rows and columns indexed by permutations u satisfying P(u) = U[([lambda]).

Let E be a proper subset of the state space and let M (E) be the corresponding

principal submatrix of M.

n] is its corresponding n x n leading

principal submatrix.

Let us also assume that A itself has been obtained as the upper left

principal submatrix [[bar.

denote the k-th order

principal submatrix of T, there is a sequence {[[lambda].