Abstract:
The concept of block determinant
\mathrmD\mathrme\mathrmt 
operation of multi-lateral matrices is explained, and the basic theorem of block determinant
\mathrmD\mathrme\mathrmt 
operation of multi-lateral matrix section is proved. Some algebraic properties of block determinant
\mathrmD\mathrme\mathrmt 
operation of multi-lateral matrices are given. As the application domain of this concept, the relationship between block determinant
\mathrmD\mathrme\mathrmt 
operation and block tracing
\mathrmT\mathrmr 
operation of multilateral matrix is explored.