On Gelfand-naimark Decomposition of a Nonsingular Matrix
نویسنده
چکیده
Let F = C or R and A ∈ GLn(F). Let s(A) ∈ R+ be the singular values of A, λ(A) ∈ C the unordered n-tuple of eigenvalues of A, a(A) := diagR ∈ R+, where A = QR is the QR decomposition of A, u(A) := diagU ∈ C, where A = LωU is any Gelfand-Naimark decomposition. We obtain complete relations between (1) u(A) and a(A), (2) u(A) and s(A), (3) u(A) and λ(A), and (4) a(A) and λ(A). We also study the relations between any three elements among u, λ, a, s.
منابع مشابه
On the Gelfand-naimark Decomposition of a Nonsingular Matrix
Let F = C or R and A ∈ GLn(F). Let s(A) ∈ R+ be the singular values of A, λ(A) ∈ C the unordered n-tuple of eigenvalues of A, a(A) := diag R ∈ R+, where A = QR is the QR decomposition of A, u(A) := diag U ∈ C, where A = LωU is any Gelfand-Naimark decomposition. We obtain complete relations between (1) u(A) and a(A), (2) u(A) and s(A), (3) u(A) and λ(A), and (4) a(A) and λ(A). We also study the ...
متن کاملAsymptotic Behavior of Gelfand-naimark Decomposition
LetX = LσU be the Gelfand-Naimark decomposition of X ∈ GLn(C), where L is unit lower triangular, σ is a permutation matrix, and U is upper triangular. Call u(X) := diagU the u-component of X. We show that in a Zariski dense open subset of the ω-orbit of certain Bruhat decomposition, lim m→∞ |u(X)| = diag (|λω(1)|, · · · , |λω(n)|). The other situations where lim m→∞ |u(X)| converge to different...
متن کاملDECOMPOSITION METHOD FOR SOLVING FULLY FUZZY LINEAR SYSTEMS
In this paper, we investigate the existence of a positive solution of fully fuzzy linear equation systems. This paper mainly to discuss a new decomposition of a nonsingular fuzzy matrix, the symmetric times triangular (ST) decomposition. By this decomposition, every nonsingular fuzzy matrix can be represented as a product of a fuzzy symmetric matrix S and a fuzzy triangular matrix T.
متن کاملSymmetrised Doubly Non Central, Nonsingular Matrix Variate Beta Distribution
In this paper, we determine the symmetrised density of a nonsingular doubly noncentral matrix variate beta type I and II distributions under different definitions.
متن کاملA stable iteration to the matrix inversion
The matrix inversion plays a signifcant role in engineering and sciences. Any nonsingular square matrix has a unique inverse which can readily be evaluated via numerical techniques such as direct methods, decomposition scheme, iterative methods, etc. In this research article, first of all an algorithm which has fourth order rate of convergency with conditional stability will be proposed. ...
متن کامل