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

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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…

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

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

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