Johnson, Charles R.; Pierce, Stephen Linear maps on Hermitian matrices: The stabilizer of an inertia class. II. (English) Zbl 0593.15021 Linear Multilinear Algebra 19, 21-31 (1986). [For part I, see Can. Math. Bull. 28, 401-404 (1985; Zbl 0577.15008)]. The authors remove the onto assumption in their previous work, proving that a nonsingular linear transformation on complex Hermitian matrices sending an inertia class into itself has the form eX*AX or \(eX*A^ tX\) except possibly for inertia classes (n,0,0),(0,n,0),(0,0,n),(n/2,n/2,0). Reviewer: K.H.Kim Cited in 20 Documents MSC: 15A63 Quadratic and bilinear forms, inner products 15B57 Hermitian, skew-Hermitian, and related matrices Keywords:stabilizer; congruence; nonsingular linear transformation; complex Hermitian matrices; inertia classes Citations:Zbl 0577.15008 PDFBibTeX XMLCite \textit{C. R. Johnson} and \textit{S. Pierce}, Linear Multilinear Algebra 19, 21--31 (1986; Zbl 0593.15021) Full Text: DOI References: [1] Choi M. D., Proc. Symp. in Pure Math. 38 pp 583– (1982) [2] DOI: 10.1080/03081088508817640 · Zbl 0557.15011 · doi:10.1080/03081088508817640 [3] Johnson C. R., Can. Math. Bull. 17 (1985) [4] DOI: 10.1007/BF01609396 · Zbl 0298.46062 · doi:10.1007/BF01609396 [5] Marcus M., Pac. J. Math. 9 pp 1215– (1959) [6] DOI: 10.1080/03081087808817237 · Zbl 0397.15011 · doi:10.1080/03081087808817237 [7] DOI: 10.1007/BF01397969 · Zbl 0158.28003 · doi:10.1007/BF01397969 [8] DOI: 10.1007/3-540-06725-6_11 · doi:10.1007/3-540-06725-6_11 [9] DOI: 10.1007/BF01617922 · Zbl 0342.46055 · doi:10.1007/BF01617922 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.