分块三角矩阵逆的存在性判定及其计算

The existence determination and calculation of the inverse of block triangular matrices

研究了分块三角矩阵可逆性的判定及其逆矩阵的表示.首先,利用分块初等矩阵的性质给出了分块上(下)三角矩阵的可逆条件及其逆矩阵的表示.然后,利用置换矩阵的性质进一步给出分块次上(下)三角矩阵的可逆条件及其逆矩阵的表示.最后,通过实例对所提计算方法进行验证.

The determination of reversibility of block triangular matrices and the representation of inverse matrices are studied.Firstly,using the properties of block elementary matrices,the invertible conditions and inverse matrix representation of block upper(lower)triangular matrices are given.Then,based on the properties of permutation matrices,the invertible conditions and inverse matrix representation of block upper(lower)triangular matrices are obtained.Finally,an example is given to verify the proposed algorithm.