The isospectral set of the Dirac matrix D=d+d* consists of orthogonal Q for which Q* D Q is an equivalent Dirac matrix. It can serve as the symmetry of a finite geometry G. The symmetry is a subset of the orthogonal group or unitary group and isospectral Lax deformations produce commuting flows d/dt D=[B(g(D)),D] on this symmetry space. In this note, we remark that like in the Toda case, D_t=Q_t* D_0 Q_t with exp(-t g(D))=Q_t R_t solves the Lax system.

翻译：狄拉克矩阵D=d+d*的等谱集由满足Q* D Q为等价狄拉克矩阵的正交矩阵Q构成。该集合可作为有限几何G的对称群。此对称群是正交群或酉群的子集，而等谱Lax形变在该对称空间上产生满足d/dt D=[B(g(D)),D]的对易流。本文指出：与Toda系统情形类似，通过关系式exp(-t g(D))=Q_t R_t定义的D_t=Q_t* D_0 Q_t可求解该Lax系统。