Fischer type determinantal inequalities for accretive–dissipative matrices
نویسندگان
چکیده
منابع مشابه
Determinantal inequalities for positive definite matrices
Let Ai , i = 1, . . . ,m , be positive definite matrices with diagonal blocks A ( j) i , 16 j 6 k , where A ( j) 1 , . . . ,A ( j) m are of the same size for each j . We prove the inequality det( m ∑ i=1 A−1 i ) > det( m ∑ i=1 (A (1) i ) −1) · · ·det( m ∑ i=1 (A (k) i ) −1) and more determinantal inequalities related to positive definite matrices.
متن کاملDeterminantal Inequalities for Block Triangular Matrices
This paper presents some results that complement (2). We believe our results are of new pattern concerning determinantal inequalities. Let us fix some notation. The matrices considered here have entries from the field of complex numbers. X ′,X ,X∗ stand for transpose, (entrywise)conjugate, conjugate transpose of X , respectively. For two n -square Hermitian matrices X ,Y , we write X > Y to mea...
متن کاملSingular value inequalities for positive semidefinite matrices
In this note, we obtain some singular values inequalities for positive semidefinite matrices by using block matrix technique. Our results are similar to some inequalities shown by Bhatia and Kittaneh in [Linear Algebra Appl. 308 (2000) 203-211] and [Linear Algebra Appl. 428 (2008) 2177-2191].
متن کاملDeterminantal and Eigenvalue Inequalities for Matrices with Numerical Ranges in a Sector
Let A = ( A11 A12 A21 A22 ) ∈ Mn, where A11 ∈ Mm with m ≤ n/2, be such that the numerical range of A lies in the set {eiφz ∈ C : |=z| ≤ (<z) tanα}, for some φ ∈ [0, 2π) and α ∈ [0, π/2). We obtain the optimal containment region for the generalized eigenvalue λ satisfying λ ( A11 0 0 A22 ) x = ( 0 A12 A21 0 ) x for some nonzero x ∈ C, and the optimal eigenvalue containment region of the matrix I...
متن کاملRandom Matrices and Determinantal Processes
Eigenvalues of random matrices have a rich mathematical structure and are a source of interesting distributions and processes. These distributions are natural statistical models in many problems in quantum physics, [15]. They occur for example, at least conjecturally, in the statistics of spectra of quantized models whose classical dynamics is chaotic, [4]. Random matrix statistics is also seen...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2013
ISSN: 0024-3795
DOI: 10.1016/j.laa.2012.11.016