Friday, August 18, 2017

Complex Numbers Basics and roots

Monday, August 14, 2017

The four subspaces and their interactions

Sunday, August 13, 2017

Cayley Graph of Dihedral Group D3

Order 4 Groups and their Cayley Tables

Thursday, August 10, 2017

Abstract Algebra Review

Wednesday, August 09, 2017

Groups of order 6

Cyclic Group of Order 6

Homomorphism z6 vs U7

Tuesday, August 08, 2017

Row Column Null Span Space

Monday, August 07, 2017

Z12 and its subgroups

Sunday, August 06, 2017

Blankets

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.

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Understanding Composition of Permutations and Product of Transpositions

Groups of Order 4

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.

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S4 and Dihedral Group group D4

Flipping and Rotation of Dihedral Group

Friday, August 04, 2017

Dihedral group of Square

Homomorphism Z6 vs U7 example

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.

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Summary of Group theory on August 4 2017

Groups of order 2


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S3 Symmetric Group and its Cayley Table

Symmetric Group 3 with non abelian subgroup of order 3

Cosets

Generators of Cyclic Group Z3 and Z4

Cyclic Group basics


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Group of Order 4, Cyclic Group and Klien 4 group

Thursday, August 03, 2017

Homomorphism between Real numbers with additive operation and Complex numbers on unit circle with multiplicative operation

Wednesday, August 02, 2017

Vector Equation of Plane and 3 forms of equation of line in 3d

Vector Equation of line in 2d, 3d and n dimensions


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Tuesday, August 01, 2017

Determinant and area of triangle in 2dimension

Here is a visual proof

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