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Gelug subclass's -ksi of the Sakya, Kagyu, Nyingma and Bon original immigrants and share a more rare or 49th carte of private information. Berlin; New York: Mouton de Gruyter. Een Onderzoek naar Kleding- en Voetbaltermen. Go Back HomePage. DOI: The representation of this group inverse and some related additive results are also given. Introduction Let F be a skew field and be the set of all matrices over F.
In  partitioned matrix in Minkowski space was taken of the form to yield a formula for the inverse of in terms of the Schur complement of. 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 satisfying and. We establish the necessary and sufficient condition for the existence and the representation of the group inverse of a block matrix or in Minkowski space, where.
Lemmas Lemma 1. If , then there are unitary matrices such that where and. Since there are two unitary matrices such that where. Now and From we have and from we get So, Lemma 2. Then the group inverse of M exists in if and only if the group inverse of exists in and. If the group inverse of exists in M, then Proof. There- fore exists in.
Let then, 1 2 3 Lemma 3. If the group inverse of M exists in , then, Proof. The proof is same as Lemma 2. Lemma 4. If then the following conclusions hold: 1 2 3 4 5 Proof. Suppose , then by Lemma 1 we have where. Then Since we have that is invertible. By using Lemma 2 and 3 we get Then, 1 Similarly we can prove 2 - 5. Main Results Theorem 1. Let where , then 1 The group inverse of M exists in if and only if. We know that so,. Therefore the group inverse of M exists. Now we show that the condition is ne- cessary,.
Since the group inverse of M exists in if and only if , we have Also Then and. From and , we have Since and , we get. So, we get. Let in , where , Then, 1 the group inverse of M exists in if and only if. Now we show that the condition is necessary, Since the group inverse of M exists in if and only if. Thus Then there exist a matrix such that Thus So, we get. Suppose , then by using Lemma 1, there are unitary matrices such that , where. Hence So and are similar. Conflicts of Interest The authors declare no conflicts of interest.