Select Page ## Spanning matrix space by niltopent matrices: TIFR 2018 Part A, Problem 15

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... ## Real Symmetric matrix: TIFR 2018 Part A, Problem 6

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...

## Arithmetical Dynamics: Two possible problems

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...

## Arithmetical Dynamics: An intro:

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...