FINDING THE SKEW-SYMMETRIC SOLVENT TO A QUADRATIC MATRIX EQUATION
نویسندگان
چکیده
منابع مشابه
AN ALGORITHM FOR FINDING THE EIGENPAIRS OF A SYMMETRIC MATRIX
The purpose of this paper is to show that ideas and techniques of the homotopy continuation method can be used to find the complete set of eigenpairs of a symmetric matrix. The homotopy defined by Chow, Mallet- Paret and York [I] may be used to solve this problem with 2""-n curves diverging to infinity which for large n causes a great inefficiency. M. Chu 121 introduced a homotopy equation...
متن کاملA Range Associated with Skew Symmetric Matrix
We study the range S(A) := {xT Ay : x, y are orthonormal in Rn}, where A is an n×n complex skew symmetric matrix. It is a compact convex set. Power inequality s(A) ≤ s(A), k ∈ N, for the radius s(A) := maxξ∈S(A) |ξ| is proved. When n = 3, 4, 5, 6, relations between S(A) and the classical numerical range and the k-numerical range are given. Axiomatic characterization of S(A) is given. Sharp poin...
متن کاملThe symmetric linear matrix equation
In this paper sufficient conditions are derived for the existence of unique and positive definite solutions of the matrix equations X−A1XA1− . . .−A∗mXAm = Q and X+A1XA1+ . . .+ A∗mXAm = Q. In the case there is a unique solution which is positive definite an explicit expression for this solution is given.
متن کاملSymmetric Matrix Polynomial Equation
A new numerical procedure is proposed to solve the symmetric matrix polynomial equation A T (?s)X(s) + X T (?s)A(s) = 2B(s) that is frequently encountered in control and signal processing. It is based on interpolation and takes fully advantage of symmetry of the equation by reducing the original problem dimension. The algorithm is more eecient and more general than older methods and, namely, it...
متن کاملEla Structured Canonical Forms for Products of (skew-)symmetric Matrices and the Matrix Equation Xax = B
The contragredient transformation A 7→ PAP, B 7→ PBP of two matrices A,B effects simultaneous similarity transformations of the products AB and BA. This work provides structured canonical forms under this transformation for symmetric or skew-symmetric A,B. As an application, these forms are used to study the quadratic matrix equation XAX = B, where both A,B are skew-symmetric or symmetric matri...
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: East Asian mathematical journal
سال: 2012
ISSN: 1226-6973
DOI: 10.7858/eamj.2012.044