We make a comparison between the identity matrix and the counteridentity matrix by studying the eigensystem of $J+M$, where $J$ is the counteridentity matrix and $M$ is a structured matrix, with the goal of expressing this system entirely in terms of the corresponding eigensystem of $M$. Also, properties of some parametric families of the form $J+\rho M$ are studied.
"On the Counteridentity Matrix." Missouri J. Math. Sci. 17 (1) 26 - 34, Winter 2005. https://doi.org/10.35834/2005/1701026