Any explanations of the attached definitions is greatly appreciated. Thank you.
The definition of the minimal polynomial for the linear transformation....
the relationship between the cosets in G of the stabilizer....
Please see the attachment.
(a) For linear transformation , we define
Then the minimal polynomial of is the monic polynomial which generates .
In another word, the minimal polynomial is the monic polynomial at the least
degree in .
For example, maps from to . ...
This explains the definition of a minimal polynomial for a linear transformation and the relationship between cosets in the stabilizer.