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Departemen Matematika FMIPA Universitas Padjadjaran, Jl. Raya Bandung-Sumedang Km. 21, Jatinangor-Sumedang 45363

### Dr. Sisilia Sylviani, M.Si

Asisten Ahli

Course Lectures

• Aljabar Linear
• Aljabar Linear Terapan
• Matematika Diskrit
• Logika Matematika

Reseach Interest :

• Behavior theory
• Algebra of population Growth
• Computational Algebra
• Linear algebra preserver problem

Research Summary:

My research is engaged in linear algebra. especially in linear algebra and its applications. Some topics that have been the focus of my research in the past 6 years are behavior theory that related to linear control theory, the application of linear algebra in population growth problems, the use of software in learning linear algebra, and what is currently being the focus of my research is the preserver problem. A little description of Preserver problem is one topic that is very popular in topik especially in operator theory and functional analysis. These problems deal with linear maps between algebras that, roughly speaking, preserve certain properties; the goal is to ﬁnd the form of these maps. This is indeed a rather vague description, and certainly one could explain what is a linear preserver problem in a more precise and systematic manner. One example of the problem is as stated in Functional Identities by Matej BrešarMikhail, A. Chebotar, and Wallace S. Martindale. An invertibility preserving map is a map that sends invertible elements into invertible elements — ﬁnding all surjective invertibility preserving linear maps between semisimple unital Banach algebras is an intriguing open problem (the conjecture is that, up to a multiple by an invertible element, they all are Jordan homomorphisms). An idempotent preserving map is a map that sends idempotents into idempotents

—  clearly  Jordan  homomorphisms  preserve  idempotents,  and  in  algebras  having  “enough”

idempotents  it often  turns  out that  these  are the only    idempotent preserving  linear maps.  A

commutativity preserving map is a map that sends commuting pairs of elements into commuting pairs

—  homomorphisms  and  antihomomorphisms  are  obvious  examples,  but so  are  maps  having  a commutative.

range.