Abstract
In this paper, Umbrella matrices are defined which are selected from GL (n, |^ ) and it i» shown that Umbrella matrices form a matrix group with respect to the matrix product. Next, a characterization of Umbrella matrices is given; among these it İs proved that the gro up of Umbrella matices which are selected from O (n) and the group of Doubly Umbrella matrices are subgroup of Umbrella matrices which are selected from GL (n, Later it is shown that this matrix group is a Lie subgroup of GL (n, and a characteristic property is given about this Lie group. Finally it is shown that, the Lie group under consideration is not connected and noncompact are shown. At the end of this work, the Maurer-Cartan forms are investigated and using the prin- cipal I-forms the dimension of the Lie group under consideration is computed.
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