Understand the problem The set of nilpotent matrices in (M_3(R)) spans (M_3(R)) considered as an R-vector space (a matrix A is said to be nilpotent if there exists n ∈ N such that (A^n = 0)). Source of the problem TIFR 2018 Part A, Problem 15 Topic LINEAR ALGEBRA...

Understand the problem True or false: Let be a real symmetric matix s.t . Then Source of the problem TIFR 2018 Part A, Problem 6 Topic Linear Algebra Difficulty Level Medium Suggested Book Linear Algebra, Hoffman and Kunze Start with hints Hint 0Hint 1Hint 2Hint 3Hint...

1.1. Existence of (pre)Periodic Points. These are the topics expanding on I.N. Baker’s theorem. Related reading: (1) Silverman Arithmetic of Dynamical Systems: p 165. Bifurcation polynomials. Exercise 4.12 outlines some known properties and open questions (** = open...

Arithmetic dynamics is a field that amalgamates two areas of mathematics, discrete dynamical systems and number theory. Classically, discrete dynamics refers to the study of the iteration of self-maps of the complex plane or real line. Arithmetic dynamics is the study...