TY - JOUR
T1 - An extension problem for H-unitary matrices with applications to Hermitian Toeplitz matrices
AU - Freund, Roland
AU - Huckle, Thomas
PY - 1988/9
Y1 - 1988/9
N2 - Given a Hermitian matrix H, a matrix U is said to be H-unitary if UHHU = H. We consider the following extension problem: If U0 is a rectangular matrix such that UH0HU0 = A, where A is a leading principal submatrix of H, can U0 be extended to an H-unitary matrix? After presenting necessary conditions for a more general situation, we state a necessary and sufficient criterion for this problem and give a description of all its solutions. Finally, these results are used to derive some properties of factorizations of Hermitian Toeplitz matrices.
AB - Given a Hermitian matrix H, a matrix U is said to be H-unitary if UHHU = H. We consider the following extension problem: If U0 is a rectangular matrix such that UH0HU0 = A, where A is a leading principal submatrix of H, can U0 be extended to an H-unitary matrix? After presenting necessary conditions for a more general situation, we state a necessary and sufficient criterion for this problem and give a description of all its solutions. Finally, these results are used to derive some properties of factorizations of Hermitian Toeplitz matrices.
UR - https://www.scopus.com/pages/publications/45449121234
U2 - 10.1016/0024-3795(88)90189-9
DO - 10.1016/0024-3795(88)90189-9
M3 - Article
AN - SCOPUS:45449121234
SN - 0024-3795
VL - 108
SP - 213
EP - 230
JO - Linear Algebra and Its Applications
JF - Linear Algebra and Its Applications
IS - C
ER -