Gerald Bourgeois

activity

20062014

most citedHow to solve the matrix equation XA-AX=f(X)

2 citations · 3 across the 10 of their papers we have counts for

collaborators

12 papers

math.RA2014

The matrix equation $X A - A X = f (X)$ when $A$ is diagonalizable

Gerald Bourgeois

$K$ is an algebraically closed field with characteristic $0$ and $f$ is a polynomial or a holomorphic function. We study all solutions of the equation $X A - A X = f (X)$ , in the unknown…

math.RA2014

The matrix equations $X A - A X = X^{α} g (X)$ over fields or rings

Gerald Bourgeois

Let $n, α \geq 2$ . Let $K$ be an algebraically closed field with characteristic $0$ or greater than $n$ . We show that the dimension of the variety of pairs $(A, B) \in M_{n} (K)^{2}$ , wit…

math.RA2013

Nonsymmetric generic matrix equations

Gerald Bourgeois

Let $(A_{i})_{0 \leq i \leq k}$ be generic matrices over $Q$ , the field of rational numbers. Let $K = Q (E)$ , where $E$ denotes the entries of the $(A_{i})_{i}$ , and let $\o…

math.RA2012

About the matrix function X->AX+XA

Gerald Bourgeois

Let K be an infinite field such that its characteristic is not 2. We show that, for every $A \in M_{n} (K)$ such that $rank (A) \geq n /2$ , there exists $B\in\mathcal{M}…

math.RA2012

Common Invariant Subspace and Commuting Matrices

Gerald Bourgeois

Let $K$ be a perfect field, $L$ be an extension field of $K$ and $A, B \in M_{n} (K)$ . If $A$ has $n$ distinct eigenvalues in $L$ that are explicitly known, then we can check i…

math.RA2011

Commmuting exponentials in dimension at most 3

Gerald Bourgeois

Let A,B be two square complex matrices of dimension at most 3. We show that the following conditions are equivalent i) There exists a finite subset U included in {2,3,4,...} such t…

The matrix equation XA−AX=f(X) when A is diagonalizable

The matrix equations XA−AX=Xαg(X) over fields or rings

Nonsymmetric generic matrix equations

About the matrix function X->AX+XA

Common Invariant Subspace and Commuting Matrices

Commmuting exponentials in dimension at most 3

The matrix equation $X A - A X = f (X)$ when $A$ is diagonalizable

The matrix equations $X A - A X = X^{α} g (X)$ over fields or rings