What is another word for companion matrix?
Pronunciation: [kəmpˈani͡ən mˈe͡ɪtɹɪks] (IPA) 
The term companion matrix refers to a particular type of square matrix where the main diagonal consists of zeros and the sub-diagonal is composed of the coefficients of a given polynomial. There are a variety of synonyms for this definition, including polynomial matrix, associated matrix, characteristic matrix, coefficient matrix, and companion polynomial matrix. While these terms may differ in their technical usage or emphasis on specific mathematical concepts, they all ultimately refer to the same type of matrix. Companion matrices are often used in applications such as linear algebra, control theory, and algebraic geometry, and understanding the various synonyms for this concept can help to clarify their use in different contexts.
