Abstract
Necessary and sufficient conditions for the existence of the group inverse of the block matrix in Minkowski Space are studied, where are both square and . The representation of this group inverse and some related additive results are also given.
Highlights
Open AccessLet F be a skew field and F n×n ( ) be the set of all matrices over F
The research on the existence and the representation of the group inverse for block matrices in Euclidean space has been done in wide range
In [13] necessary and sufficient condition for the existence of Re-nnd solution has been established of the matrix equation AXA~ = C where
Summary
Let F be a skew field and F n×n ( ) be the set of all matrices over F. The research on the existence and the representation of the group inverse for block matrices in Euclidean space has been done in wide range. For the literature of the group inverse of block matrix in Euclidean space, see [5]-[11]. In [13] necessary and sufficient condition for the existence of Re-nnd solution has been established of the matrix equation AXA~ = C where. Minkowski Space is an indefinite inner product space in which the metric matrix associated with the indefinite inner product is denoted by G and is defined as. The representation of the group inverse of a block matrix or ( ) ( ) in Minkowski space, where P~ ,Q~ ∈ K n×n , rank Q~ ≥ rank P~.
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