Linear groups represent an important study 0 f Lie groups. These locally compact groups are important in the study of representation theory. They are noticeable in the study of vector spaces and topological Spaces. Applications of linear Groups Can be seen in their relation to inner products and normal matrices. The basic concepts of linear groups are investigated to give a foundation for further, more advanced, study in this field. Special attention is paid to unitary, orthogonal and hermitian matrices. Inner products, congruence and conjunctive equivalence in relation to the above matrices are also discussed
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