Groups and Symmetry pp 44-51 | Cite as

# Matrix Groups

Chapter

## Abstract

The set of all invertible
Matrix multiplication is associative, the

*n*×*n*matrices with real numbers as entries forms a group under matrix multiplication. We recall that if*A*= (*a*_{ ij }),*B*= (*b*_{ ij }) are two such matrices, the*ij*th entry of the*product AB*is the sum$${a_{i1}}{b_{1j}} + {a_{i2}}{b_{2j}} + \cdot \cdot \cdot + {a_{in}}{b_{nj}}$$

*n*×*n*identity matrix*I*_{ n }plays the role of identity element, and the above product*AB*is invertible with inverse*B*^{−l}*A*^{−1}.## Keywords

Matrix Multiplication Unitary Matrice Matrix Group Invertible Matrice Integer Entry
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## Copyright information

© Springer Science+Business Media New York 1988