### Complex Numbers Basics and roots

Labels: basics, Complex Numbers, Real Analysis

This is a short piece to summarize whats going in my life.

Labels: Column Space, Linear Algebra, Null Space, Orthogonal, Subspace

I searched through my archives and I had read this book 8 years back on Jan 20,2009. I had got this book from Carbondale Library. So rereading again was fun on my iPad. It's a story about Author Craig Thompson's first love and his overly religious family. His chilhood and growing up in cold Wisconsin. Being bullied at school and finding his first girlfriend at a church camp. Being head over heels and after doing all the cutesy stuff he decides to visit her for two weeks in the midst of her parents getting divorced. She has three other siblings, two of them adopted and taking care of her sister's daughter. Both her adopted siblings have their own struggles. On his return from the reunion they grow apart and he gets rid of her presents and memories and movies to city to pursue his passion of art and discovers city life away from the religious upbringing which has tormented him throughout his high school years. Though his parents still remain very relgious.

Labels: Graphic Novel

Labels: Abstract Algebra, Composition, Cyclic, Groups, Transposition

For Order 4 there are basically two types of group. Klien 4 and Cyclic Group of order 4. In Klien 4 each element is its own inverse. In cyclic group there are two elements which are inverse of each other and there are two which are their own inverses. The two which are inverse of each other are also the generator of this cyclic group.

Labels: Abelian, Abstract Algebra, Cyclic, Klien 4, Subgroup

Labels: Abstract Algebra, Cyclic, Dihedral, Permutation, Subgroup, Symmetric Group

One should notice that just finding a bijective mapping doesn't define a homomorphism (or isomorphism). The mapping should satisfy f(x+y)=f(x)*f(y) to be a homomorphism.

Labels: Abstract Algebra, Bijection, Example, Function, Homomorphism, Proof

Labels: Composition, Dihedral, Groups, Non Abelian, S3, Subgroup, Symmetric Group

Labels: Abstract Algebra, Complex Numbers, Homomorphism, Real Numbers

Labels: Calculus, Line, Linear Algebra, Plane, Vector

Labels: Abstract Algebra, Determinant, Linear Algebra, Proof