University of Macau Abstract Equality cases of some Hölder-type norm inequalities by Leong Sok I Thesis Supervisor: Prof, Cheng Che Man Master of Science in Mathematics In this thesis, we study the equality cases of some Hölder-type norm inequalities in matrix spaces. Though the inequalities are known, their equality cases are not given in literature and do not follow directly from the proofs. In this thesis, we characterize their equality cases.