Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Let A and C be square complex matrices of size n, the C-determinantal range of A is the subset of the complex plane { det ( A - U C U * ) : U U * = I n } . If A, C are both Hermitian matrices, then by a result of Fiedler (1971) 11 this set is a real line segment.In our paper  study this set for the case when C is a Hermitian matrix. Our purpose is to revisit and improve two ll-known results on this topic. The first result is due to Li concerning the C-numerical range of a Hermitian matrix, see Condition 5.1?(a) in Li, (1994) 20. The second one is due to C.-K. Li, Y.-T. Poon and N.-S. Sze about necessary and sufficient conditions for the C-determinantal range of A to be a subset of the line, (see Li et?al. (2008) 21, Theorem 3.3).
['Alexander E. Guterman', 'R. Lemos', 'Graça Soares']
I am writing a research paper on a idea On the C-determinantal range for special classes of matrices
[{"from": "human", "value": "I am writing a research paper on a idea On the C-determinantal range for special classes of matrices"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Let A and C be square complex matrices of size n, the C-determinantal range of A is the subset of the complex plane { det ( A - U C U * ) : U U * = I n } . If A, C are both Hermitian matrices, then by a result of Fiedler (1971) 11 this set is a real line segment.In our paper  study this set for the case when C is a Hermitian matrix. Our purpose is to revisit and improve two ll-known results on this topic. The first result is due to Li concerning the C-numerical range of a Hermitian matrix, see Condition 5.1?(a) in Li, (1994) 20. The second one is due to C.-K. Li, Y.-T. Poon and N.-S. Sze about necessary and sufficient conditions for the C-determinantal range of A to be a subset of the line, (see Li et?al. (2008) 21, Theorem 3.3)."}]