turkmath.org

In this talk We will discuss several well known asymptotic matrix result, namely, Beurling-Gelfand-Yamamoto Theorem about the spectral norm and the spectral radius of a square matrix, Francis-Kublanovskaja QR algorithm and Rutishauser LR algorithmon the numerical computation of eigenvalues of a square matrix, Aluthge iteration regarding the polar decomposition, and their extensions in the context of semisimple Lie groups. I hope to bring out some good flavor and relate different areas of mathematics including differential geometry, Lie group, matrix theory, numerical analysis, and topology in this talk.