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Linear and Multilinear Algebra Volume 17, 1985 - Issue 1
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Original Articles

Signature preserving linear maps of Hermitian matrices

J. W. Helton Dept. of Mathematics, University of California, San Diego, La Jolla, CA, 92093, USA
&
L. Rodman School of Mathematical Sciences, Tel-Aviv University, Tel-Aviv, Israel
Pages 29-37 | Received 05 Jan 1984, Accepted 05 Apr 1984, Published online: 30 May 2007

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Read on this site (6)

Sean Clark, Chi-Kwong Li, Jennifer Mahle & Leiba Rodman. (2009) Linear preservers of higher rank numerical ranges and radii. Linear and Multilinear Algebra 57:5, pages 503-521.
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Raphael Loewy. (1992) Chapter 3:inertia preservers. Linear and Multilinear Algebra 33:1-2, pages 23-30.
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M. H. Lim. (1992) Chapter 2:rank and tensor rank. Linear and Multilinear Algebra 33:1-2, pages 7-21.
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Charles R. Johnson, Chi-Kwong Li, Leiba Rodman, Ilya Spitkovsky & Stephen Pierce. (1992) Linear maps preserving regional eigenvalue location. Linear and Multilinear Algebra 32:3-4, pages 253-264.
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Chi-Kwong Li & Nam-Kiu Tsing. (1988) Linear operators preserving the decomposable numerical radius. Linear and Multilinear Algebra 23:4, pages 333-341.
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Charles R. Johnson & Stephen Pierce. (1986) Linear maps on Hermitian matrices: the stabilizer of an inertia class, II. Linear and Multilinear Algebra 19:1, pages 21-31.
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Articles from other publishers (12)

Wai-Shun Cheung, Chi-Kwong Li & Yiu-Tung Poon. (2009) Isometries between matrix algebras. Journal of the Australian Mathematical Society 77:1, pages 1-16.
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Peter Šemrl. (2003) Hua’s fundamental theorems of the geometry of matrices and related results. Linear Algebra and its Applications 361, pages 161-179.
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Raphael Loewy & Stephen Pierce. (1995) Linear preservers of balanced nonsingular inertia classes. Linear Algebra and its Applications 223-224, pages 483-499.
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Raphael Loewy & Stephen Pierce. (1994) Linear preservers of balanced singular inertia classes. Linear Algebra and its Applications 201, pages 61-77.
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Ehud Moshe Baruch & Raphael Loe. (1993) Linear preservers on spaces of hermitian or real symmetric matrices. Linear Algebra and its Applications 183, pages 89-102.
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Ehud Moshe Baruch & Raphael Loewy. (1992) Rank preservers and inertia preservers on spaces of Hermitian matrices. Linear Algebra and its Applications 167, pages 209-212.
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Roger A. Horn, Chi-Kwong Li & Nam-Kiu Tsing. (1991) Linear Operators Preserving Certain Equivalence Relations on Matrices. SIAM Journal on Matrix Analysis and Applications 12:2, pages 195-204.
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Raphael Loewy. (1990) Linear maps which preserve a balanced nonsingular inertia class. Linear Algebra and its Applications 134, pages 165-179.
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Matjaž Omladič. (1990) On operators preserving the numerical range. Linear Algebra and its Applications 134, pages 31-51.
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Raphael Loewy. (1990) Linear Maps That Preserve an Inertia Class. SIAM Journal on Matrix Analysis and Applications 11:1, pages 107-112.
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Raphael Loewy. (1989) Linear transformations which preserve or decrease rank. Linear Algebra and its Applications 121, pages 151-161.
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Stephen Pierce & Leiba Rodman. (1988) Linear Preservers of the Class of Hermitian Matrices with Balanced Inertia. SIAM Journal on Matrix Analysis and Applications 9:4, pages 461-472.
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