# Minimal polynomial and stabilizer

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....

https://brainmass.com/math/linear-transformation/minimal-polynomial-stabilizer-172613

#### Solution Preview

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 . ...

#### Solution Summary

This explains the definition of a minimal polynomial for a linear transformation and the relationship between cosets in the stabilizer.

$2.19