# Euclidean Group : Forming a Group under Matrix Multiplication

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The Euclidean group is defined as

E3 ={X R 4 4 | X = , R O3, t R 3}

Where

O3 is a 3 3 orthogonal matrix, therefore R is an element in O3.

R 4 4 means real 4 4 matrix vector space.

R 3 means real 3-dimensional vector space.

0 in the is 0 0 0, so that X is a 4 4 matrix.

Show the set E3 forms a group under matrix multiplication.

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The Euclidean group is defined as

E3 ={X R 4 4 | X = , R O3, t R 3}

Where

O3 is a 3 3 orthogonal matrix, therefore R is an element in O3.

R 4 4 means real 4 4 matrix vector space.

R 3 means real 3-dimensional vector space.

0 in the ...

#### Solution Summary

A Euclidean group is investigated. The solution is detailed.