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| − | The left coset gH means that you take <math> g | + | The left coset gH means that you take <math> g \bullet H </math> where <math> \bullet </math> is whatever the current operator is (+, *, etc.). The right and left cosets could agree however, not always. For example, in instances where H contains matrices the right and left cosets may not agree. |
Latest revision as of 16:23, 21 September 2008
I am a little confused about cosets. I know that the left coset is represented by aH in the book and the right coset is represented by Ha. What is the significance if it is the left or right coset? How does that affect how you work with them?
nshafer
The left coset gH means that you take $ g \bullet H $ where $ \bullet $ is whatever the current operator is (+, *, etc.). The right and left cosets could agree however, not always. For example, in instances where H contains matrices the right and left cosets may not agree.
