Solutions of the Matrix Equation AX + YB = C with Triangular Coefficients

نویسندگان

چکیده

We establish necessary and sufficient conditions for the existence of triangular solutions a linear matrix equation AX + YB = Cover commutative ring principal ideals whose coefficients A, B , C are matrices. It is also shown that there no this kind all which triangular.

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Diagonal and Monomial Solutions of the Matrix Equation AXB=C

In this article, we consider the matrix equation $AXB=C$, where A, B, C are given matrices and give new necessary and sufficient conditions for the existence of the diagonal solutions and monomial solutions to this equation. We also present a general form of such solutions. Moreover, we consider the least squares problem $min_X |C-AXB |_F$ where $X$ is a diagonal or monomial matrix. The explici...

متن کامل

determinant of the hankel matrix with binomial entries

abstract in this thesis at first we comput the determinant of hankel matrix with enteries a_k (x)=?_(m=0)^k??((2k+2-m)¦(k-m)) x^m ? by using a new operator, ? and by writing and solving differential equation of order two at points x=2 and x=-2 . also we show that this determinant under k-binomial transformation is invariant.

15 صفحه اول

On the Matrix Equation Xa − Ax = X

We study the matrix equation XA − AX = X p in M n (K) for 1 < p < n. It is shown that every matrix solution X is nilpotent and that the generalized eigenspaces of A are X-invariant. For A being a full Jordan block we describe how to compute all matrix solutions. Combinatorial formulas for A m X ℓ , X ℓ A m and (AX) ℓ are given. The case p = 2 is a special case of the algebraic Riccati equation.

متن کامل

Integer Solutions of the Equation y 2 = Ax 4 + B

Let A ∈ {k2(k2l2 + 1), 4k2(k2(2l − 1)2 + 1)}, where k and l are positive integers, and let B be a non-zero square-free integer such that |B| < √ A. In this paper we determine all the possible integer solutions of the equation y2 = Ax4 + B by using terms of Lucas sequences of the form mx2.

متن کامل

Norm Estimates for Solutions of Matrix Equations Ax − Xb = C and X − Axb = C

Let A, B and C be matrices. We consider the matrix equations Y − AY B = C and AX −XB = C. Sharp norm estimates for solutions of these equations are derived. By these estimates a bound for the distance between invariant subspaces of matrices is obtained.

متن کامل

ذخیره 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: Journal of Mathematical Sciences

سال: 2022

ISSN: ['1072-3374', '1573-8795']

DOI: https://doi.org/10.1007/s10958-022-05734-x