AbstractWe study the matrix equation XA−AX=Xp in Mn(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 AmXℓ, XℓAm and (AX)ℓ are given. The case p=2 is a special case of the algebraic Riccati equation
Let P be a given Hermitian matrix satisfying P2=I. Using the eigenvalue decomposition of P, we consi...
AbstractWe consider the matrix equation X = Q + NX−1N∗. Its Hermitian solutions are parametrized in ...
AbstractThe main concern of this paper is linear matrix equations with block-companion matrix coeffi...
We solve the quadratic matrix equation AXA = XAX with a given nilpotent matrix A, to find all commut...
Let A be a nilpotent matrix of index two, and consider the Yang–Baxter-like matrix equation AXA=XAX....
AbstractWe study the matrix equation Xn=A in M2(Z) for given A and n ϵ N. If A ≠ aI for integer a, t...
AbstractWe consider the matrix equation X = Q + NX−1N∗. Its Hermitian solutions are parametrized in ...
Let A be a nilpotent matrix of index three and consider the Yang–Baxter-like matrix equation AXA=XAX...
Let A be a nilpotent matrix of index three and consider the Yang–Baxter-like matrix equation AXA=XAX...
AbstractSimple necessary and sufficient conditions for the matrix equation X + ATX−1A = I to have a ...
AbstractThis paper is concerned with the determination of algebraic formulae giving all the solution...
This chapter provides a survey of the main theoretical properties concerning algebraic Riccati equat...
This chapter provides a survey of the main theoretical properties concerning algebraic Riccati equat...
For the pair of matrix equations AX = C, XB = D this paper gives common solutions of minimum possibl...
AbstractThis paper deals with the matrix equation f(X)=A, where A∈Cn×n is a given matrix, and ƒ is a...
Let P be a given Hermitian matrix satisfying P2=I. Using the eigenvalue decomposition of P, we consi...
AbstractWe consider the matrix equation X = Q + NX−1N∗. Its Hermitian solutions are parametrized in ...
AbstractThe main concern of this paper is linear matrix equations with block-companion matrix coeffi...
We solve the quadratic matrix equation AXA = XAX with a given nilpotent matrix A, to find all commut...
Let A be a nilpotent matrix of index two, and consider the Yang–Baxter-like matrix equation AXA=XAX....
AbstractWe study the matrix equation Xn=A in M2(Z) for given A and n ϵ N. If A ≠ aI for integer a, t...
AbstractWe consider the matrix equation X = Q + NX−1N∗. Its Hermitian solutions are parametrized in ...
Let A be a nilpotent matrix of index three and consider the Yang–Baxter-like matrix equation AXA=XAX...
Let A be a nilpotent matrix of index three and consider the Yang–Baxter-like matrix equation AXA=XAX...
AbstractSimple necessary and sufficient conditions for the matrix equation X + ATX−1A = I to have a ...
AbstractThis paper is concerned with the determination of algebraic formulae giving all the solution...
This chapter provides a survey of the main theoretical properties concerning algebraic Riccati equat...
This chapter provides a survey of the main theoretical properties concerning algebraic Riccati equat...
For the pair of matrix equations AX = C, XB = D this paper gives common solutions of minimum possibl...
AbstractThis paper deals with the matrix equation f(X)=A, where A∈Cn×n is a given matrix, and ƒ is a...
Let P be a given Hermitian matrix satisfying P2=I. Using the eigenvalue decomposition of P, we consi...
AbstractWe consider the matrix equation X = Q + NX−1N∗. Its Hermitian solutions are parametrized in ...
AbstractThe main concern of this paper is linear matrix equations with block-companion matrix coeffi...
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