Generalized interlacing inequalities

References

• Bhatia , R . 1987 . Perturbation Bounds for Matrix Eigenvalues, Pitman Research Notes in Mathematics, Vol. 162 , New York : Longman Scientific and Technical .
   Google Scholar
• Carlson , D and Marques de Sa , E . 1984 . Generalized minimax and interlacing theorems . Linear Multilinear Algebra , 15 : 77 – 103 .
   Google Scholar
• Choi , MD . 1975 . Completely positive linear maps on complex matrices . Linear Algebra Appl. , 10 : 285 – 290 .
   Web of Science ®Google Scholar
• Choi , MD , Giesinger , M , Holbrook , JA and Kribs , DW . 2008 . Geometry of higher-rank numerical ranges . Linear Multilinear Algebra , 56 : 53 – 64 .
   Web of Science ®Google Scholar
• Choi , MD , Johnston , N and Kribs , DW . 2009 . The multiplicative domain in quantum error correction . J. Phys. A Math. Theor. , 42 : 245303
   Web of Science ®Google Scholar
• Choi , MD , Kribs , DW and Życzkowski , K . 2006 . Quantum error correcting codes from the compression formalism . Rep. Math. Phys. , 58 : 77 – 91 .
   Web of Science ®Google Scholar
• Fan , K and Pall , G . 1957 . Imbedding conditions for Hermitian and normal matrices . Canad. J. Math. , 9 : 298 – 304 .
   Google Scholar
• Fulton , W . 2000 . Eigenvalues, invariant factors, highest weights, and Schubert calculus . Bull. Amer. Math. Soc. , 37 : 209 – 249 .
   Web of Science ®Google Scholar
• Horn , RA and Johnson , CR . 1991 . Topics in Matrix Analysis , Cambridge : Cambridge University Press .
   Google Scholar
• Ikramov , KD and Elsner , L . 1998 . On normal matrices with normal principal submatrices . J. Math. Sci. , 89 : 1631 – 1651 .
   Google Scholar
• Kribs , DW , Laflamme , R , Poulin , D and Lesosky , M . 2006 . Operator quantum error correction . Quantum Inform. Comput. , 6 : 382 – 399 .
   Web of Science ®Google Scholar
• Li , CK and Li , RC . 2005 . A note on eigenvalues of perturbed Hermitian matrices . Linear Algebra Appl. , 395 : 183 – 190 .
   Web of Science ®Google Scholar
• Li , CK and Mathias , R . 1999 . The Lidskii–Mirsky–Wielandt Theorem: Additive and multiplicative versions . Numer. Math. , 81 ( 3 ) : 377 – 413 .
   Web of Science ®Google Scholar
• Li , CK , Poon , YT and Sze , NS . 2009 . Condition for the higher rank numerical range to be non-empty . Linear Multilinear Algebra , 57 : 365 – 368 .
   Web of Science ®Google Scholar
• Li , CK and Sze , NS . 2008 . Canonical forms, higher rank numerical ranges, totally isotropic subspaces, and matrix equations . Proc. Am. Math. Soc. , 136 : 3013 – 3023 .
   Web of Science ®Google Scholar
• Li , CK and Tsing , NK . 1991 . On the kth matrix numerical range . Linear Multilinear Algebra , 28 : 229 – 239 .
   Google Scholar
• Malamud , SM . 2005 . Inverse spectral problem for normal matrices and the Gauss–Lucas theorem . Trans. AMS , 357 : 40 – 43 .
   Web of Science ®Google Scholar
• Marshall , AW and Olkin , I . 1979 . Inequalities: Theory of Majorization and its Applications , New York, London : Academic Press, Inc. .
   Google Scholar
• Mirsky , L . 1958 . Matrices with prescribed characteristic roots and diagonal elements . J. London Math. Soc. , 33 : 14 – 21 .
   Google Scholar
• Nielsen , MA and Chuang , IL . 2000 . Quantum Computation and Quantum Information , Cambridge : Cambridge University Press .
   Google Scholar
• Savchenko , SV . 2006 . Normal matrices and their principal submatrices of co-order one . Linear Algebra Appl. , 419 : 556 – 568 .
   Web of Science ®Google Scholar
• Stewart , G and Sun , JG . 1990 . Matrix Perturbation Theory , Boston : Academic Press .
   Google Scholar
• Thompson , RC . 1966 . Principal submatrices of normal and Hermitian matrices . Illinois J. Math. , 10 : 296 – 308 .
   Web of Science ®Google Scholar