This paper examines experimental and algorithmic contributions of advanced calculators (graphing and computer algebra system, CAS) in teaching the concept of "diagonalization," one of the key topics in Linear Algebra courses taught at the undergraduate level. Specifically, the proposed hypothesis of this study is to assess the effective utilization of advanced calculators as an assistance tool in furthering the conceptual understanding of diagonalization. To this end, using some instructional materials, we present a new dimension of teaching as a combination of a theoretical experimentation and algorithmic approach. The primary findings indicate that advanced calculators provide carefully designed tasks in favor of the acquisition of mathematical knowledge while facilitating the students' perception of the concept, both valuable tools in the instructional delivery of "diagonalization" as a concept. (Contains 6 figures and 3 tables.)