differential equation of the square root of a matrix I am wondering why the trajectory lies in the commutant of the algebra generated by A and B. Consider $M(dt)$ where $dt$ is an infinitismal time step. $M(dt)=M(0)+A.M(0).B.dt$ why does this commute with $A$ and $B$ if $M(0)$ does ?
Mathematical problems having rational number solutions @AndréNicolas In Diophantine problems, you narrow the domain of solutions right from the beginning to integers or rational numbers. What I am asking about is when the only solutions are rationals.
Mathematical problems having rational number solutions @orlandpm An example of such problems would be, if it exists, polynomials having only rational roots. I am aware that some 2nd order polynomials with rational coefficients do so. I am seeking a more general class of problems.
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