# principal submatrix

## principal submatrix

[¦prin·səpəl səb′ma·triks]
(mathematics)
An m × m matrix, P, is an m × m principal submatrix of an n × n matrix, A, if P is obtained from A by removing any n-m rows and the same n-m columns.
References in periodicals archive ?
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.
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