四元数正则矩阵束广义特征值反问题

The Inverse Generalized Eigenvalue Problem of Regular Mtrices Pencil of Quaternions

对于任意给定的X∈Qn×m,∧=diag(λ1,…,λm)∈Rm×m,利用奇异值分解、谱分解及QR分解分别给出了满足AX=BX∧,及XHBX=Im,AX=BX∧,的正则矩阵束(A,B)的通解表达式.

For any X ∈ Q^n×m, ∧ = diag（λ1 ,… ,λm） ∈ R^m×m, the general solution expressions of regular matrix pencil （A,B） which satisfy AX = BX ∧ or X^H BX = Ⅰm,AX = BX ∧ were presented by using singular value decomposition, spectral decomposition and QR decomposition.