Professor Xie Bangjie’s contribution to matrices over skew field and its development in China. (Chinese. English summary) Zbl 1150.15300

Summary: With regard to the value and difficulty of research on matrices over skew field, Professor Xie Bangjie’s research on the matrix similarity canonical form, the weak canonical form descriptive theorem, the eigenvalue basis of centerable matrices, the determinant program and self-conjugate quaternionic matrices over a skew field in 1978 \(\thicksim\) 1982 are reviewed. Moreover, since 1980 the advancement of Chinese scholars’ study based on these above is surveyed, such as the rank of matrices, the theory of similarity canonical form, the determinant of quaternionic matrices, self-conjugate quaternionic matrices, matrix equations and generalized inverse matrices.


15-03 History of linear algebra
15B33 Matrices over special rings (quaternions, finite fields, etc.)
01A60 History of mathematics in the 20th century
15A21 Canonical forms, reductions, classification
15A15 Determinants, permanents, traces, other special matrix functions
15A09 Theory of matrix inversion and generalized inverses

Biographic References:

Xie, Bangjie