The Exploration Of The Existence Of Group Inverse For A Class Block Matrix

Due to the group inverse for block matrix is extremely important in "Generalized Inverse and its Application". At the same time, it has very important practical application value in many areas. For example, in the control theory, mathematical, system control, singular differential and difference equations and operator theory, markov chains and other disciplines of wide application. Therefore, to explore the existence and specific expression of group inverse for block matrix is an important problem of theory and application value.Based on the domestic and foreign researchers, we continue to explore the existence and specific expression of group inverse for block matrix. The main work show as follow:1. According to the method of the nature of matrix projection and the elementary decomposition, we give the existence and specific expression of group inverse for block matrices under the new condition.2. Tectonic the block matrices and give the existence and specific expression of group inverse for block matrices.3. Tectonic the block matrices and give the existence and specific expression of group inverse for block matrices.4. This paper also explores the existence of triangular matrix under certain conditions and gives the specific expression of group inverse.5. Conclude the existence of block matrices (M(?)l) under certain conditions and give the specific expression of group inverse.Finally, we give some numerical examples to illustrate our results.