2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/125757In this work we present a matrix generalization of the Euler identity about exponential representation of a complex number. The concept of matrix exponential is used in a fundamental way. We define a notion of matrix imaginary unit which generalizes the usual complex imaginary unit. The Euler-like identity so obtained is compatible with the classical one. Also, we derive some exponential representation for matrix real and imaginary unit, and for the first Pauli matrix.5 pages, research work done at R&D Dept. of Company InstitutionClassical Analysis and ODEsMathematical PhysicsGeneral MathematicsFluid DynamicsQuantum Physics15A24; 15A90text