Linear combinations of Hermitian and real symmetric matrices
نویسندگان
چکیده
منابع مشابه
On Matrices Whose Real Linear Combinations Are Nonsingular
Let A be either the real field R, or the complex field C, or the skew field Q of quaternions. Let Au A2, • ■ ■ , Ak be nXn matrices with entries from A. Consider a typical linear combination E"-iV^> with real coefficients Xy; we shall say that the set {A¡} "has the property P" if such a linear combination is nonsingular (invertible) except when all the coefficients X> are zero. We shall write A...
متن کاملCorrection to "on Matrices Whose Real Linear Combinations Are Nonsingular"
2. -, Rings with a pivotal monomial, Proc. Amer. Math. Soc. 9 (1958), 635642. 3. L. P. Belluce and S. K. Jain, Prime rings having a one-sided ideal satisfying a polynomial identity, Abstract 614-89, Notices Amer. Math. Soc. 11 (1964), p. 554. 4. N. Jacobson, Structure of rings, Amer. Math. Soc. Colloq. Publ. Vol. 37, Amer. Math. Soc, Providence, R. I., 1956. 5. I. Kaplansky, Rings with a polyno...
متن کاملA uniform object-oriented solution to the eigenvalue problem for real symmetric and Hermitian matrices
a r t i c l e i n f o a b s t r a c t We present a system of classes, SHMatrix, to deal in a unified way with the computation of eigenvalues and eigenvectors in real symmetric and Hermitian matrices. Thus, two descendant classes, one for the real symmetric and other for the Hermitian cases, override the abstract methods defined in a base class. The use of the inheritance relationship and polymo...
متن کاملCongruence of Hermitian Matrices by Hermitian Matrices
Two Hermitian matrices A, B ∈ Mn(C) are said to be Hermitian-congruent if there exists a nonsingular Hermitian matrix C ∈ Mn(C) such that B = CAC. In this paper, we give necessary and sufficient conditions for two nonsingular simultaneously unitarily diagonalizable Hermitian matrices A and B to be Hermitian-congruent. Moreover, when A and B are Hermitian-congruent, we describe the possible iner...
متن کاملUnitary Matrices and Hermitian Matrices
Unitary Matrices and Hermitian Matrices Recall that the conjugate of a complex number a + bi is a − bi. The conjugate of a + bi is denoted a+ bi or (a+ bi)∗. In this section, I’ll use ( ) for complex conjugation of numbers of matrices. I want to use ( )∗ to denote an operation on matrices, the conjugate transpose. Thus, 3 + 4i = 3− 4i, 5− 6i = 5 + 6i, 7i = −7i, 10 = 10. Complex conjugation sati...
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: 1979
ISSN: 0024-3795
DOI: 10.1016/0024-3795(79)90009-0