Monthly Archives: August 2015

if A^2 is invertible then A is also invertible

Posted on August 24, 2015 by Sumant Sumant

Saw this question at stack exchange. The proof is easy and I like these two versions is invertible which means . But and so hence is invertible The other proof was let be the inverse of which means which means … Continue reading →

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Linear Algebra: Step by Step Chapter 5

Posted on August 16, 2015 by Sumant Sumant

Definition 5.2 A transformation is called a linear transformation for all vectors and in the vector space and for any scalar we have (T preserves vector addition) (T preserves scalar multiplication) Proposition 5.3 Let and be vector spaces and and … Continue reading →

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Measure theory introduction

Posted on August 13, 2015 by Sumant Sumant

This is a three part video on Measure theory and the purpose is to make notes and understand this beautiful topic He begins this video with a simple example of discrete probability distribution of a dice. Suppose we have a … Continue reading →

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Linear Algebra Step by Step notes Chapter 4

Posted on August 12, 2015 by Sumant Sumant

Chapter 4 For a general vector space, the inner product is denoted by rather than Definition: An inner product on a real vector space is an operation which assigns to each pair of vectors and which satisfies the following axioms … Continue reading →

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2^(1/n) is irrational for n > 2

Posted on August 12, 2015 by Sumant Sumant

Theorem: is irrational for Let us assume that  which by fermat’s last theorem is impossible 🙂

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Linear Algebra Step by Step Notes Chapter 2

Posted on August 11, 2015 by Sumant Sumant

Proposition 2.1 Let and be vectors in and be real numbers (or real scalars). We have the following results Proposition 2.2 Let be a vector in . Then the vectors which satisfies property $u+(-u)=0$ is unique Proposition 2.3 Let be … Continue reading →

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