TY - JOUR
T1 - Noncommutative spectral decomposition with quasideterminant
AU - Suzuki, Tatsuo
PY - 2008/3/20
Y1 - 2008/3/20
N2 - We develop a noncommutative analogue of the spectral decomposition with the quasideterminant defined by I. Gelfand and V. Retakh. In this theory, by introducing a noncommutative Lagrange interpolating polynomial and combining a noncommutative Cayley-Hamilton's theorem and an identity given by a Vandermonde-like quasideterminant, we can systematically calculate a function of a matrix even if it has noncommutative entries. As examples, the noncommutative spectral decomposition and the exponential matrices of a quaternionic matrix and of a matrix with entries being harmonic oscillators are given.
AB - We develop a noncommutative analogue of the spectral decomposition with the quasideterminant defined by I. Gelfand and V. Retakh. In this theory, by introducing a noncommutative Lagrange interpolating polynomial and combining a noncommutative Cayley-Hamilton's theorem and an identity given by a Vandermonde-like quasideterminant, we can systematically calculate a function of a matrix even if it has noncommutative entries. As examples, the noncommutative spectral decomposition and the exponential matrices of a quaternionic matrix and of a matrix with entries being harmonic oscillators are given.
KW - Noncommutative
KW - Quasideterminant
KW - Spectral decomposition
UR - http://www.scopus.com/inward/record.url?scp=38849090531&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=38849090531&partnerID=8YFLogxK
U2 - 10.1016/j.aim.2007.09.011
DO - 10.1016/j.aim.2007.09.011
M3 - Article
AN - SCOPUS:38849090531
VL - 217
SP - 2141
EP - 2158
JO - Advances in Mathematics
JF - Advances in Mathematics
SN - 0001-8708
IS - 5
ER -