We explore two main concepts in relation to truncated composition matrices: the conditions required for the binormal and commutative properties. Both of these topics are important in linear algebra due to their connection with diagonalization. We begin with the normal solution before moving onto the more complex binormal solutions. Then we cover conditions for the composition matrix to commute with a general matrix. Finally, we end with ongoing questions for future work.
Kaiser, Hallie; O'Malley, Katy; and Weeks, Grace, "Normality Properties of Composition Matricies" (2022). Mathematics Student Projects. 3.