# Linear Algebra & Statistical Techniques

Dr.Ruchi Gupta
Seema Aggarwal
SAVITTA SAINI
Last Update September 13, 2021

Linear algebra is the branch of mathematics concerning linear equations which provides concepts which are useful to many areas of computer science. It’s really useful in Data Science when data written as vectors and then operations performed  on them in order to measure them. Linear Algebraic methods are necessary to do that.

Statistics is about collection, organization, displaying, analysis, interpretation and presentation of data

• All Students

69 Lessons56h

#### UNIT-I Elementary Row Transformations

In this lecture we will introduce elementary row transformations on matrices.

#### UNIT 1 Rank of Matrix Module-I

In this lecture we will discuss the concept of Rank of a matrix, properties and the various methods to find out the Rank of a matrix. We will also learn about the Normal form of a matrix and Nullity of a Matrix. We will have discussed the application of Rank of a Matrix.We will also solve a few problems based on the Rank of a matrix.

#### : Unit 1 Solving Linear Systems using Gaussian Elimination

In this lecture we will learn to the study of the nature of the solutions of a system of linear equations.

Problems

#### UNIT 1 Gauss Jordan Row Reduction Method

In this lecture we will learn solving the system of linear equations by Gauss Jordan Row Reduction Method .

FAQs

FAQ

FAQ

FAQ

#### UNIT 2 Non Homogeneous Linear Systems(Rank) Module -I

In this lecture we will discuss the condition for consistency and inconsistency of systems of linear equation and nature of solution of a system of non homogenous linear system of equation. We will also go through the working rule for finding the solution of the equation AX=B.

#### UNIT 2 Eigen Value & Eigen Vector Module-I & II

In this module we introduce the concept of Eigen values and Eigen vectors and its applications.

#### UNIT 2 Cayley Hamilton theorem Module-1

In this lecture, we will discuss some properties of eigen value and eigen vector and will solve a few problems based on properties of eigenvalues and eigenvectors and Cayley Hamilton theorem.

#### UNIT 2 Diagonalization of matrices Module -I

In this lecture, we will see how eigenvalues and eigenvectors can be used to determine whether a square matrix is diagonalizable or not. We will also discuss the properties and application of diagonalization.

FAQ

Faq on unit 2

FAQ

FAQ

#### UNIT3 Vector Subspaces -II

Algebra of Subspaces

#### UNIT3 Linear combination of vectors

To know what is linear combination of vectors

#### :UNIT3 Span of a Set

To understand span of a set

#### Unit 3 Linear Independece of vectors

To study about linear independence and linear depence of vectors

FAQ 2

#### UNIT3 Linear Independence and Dependence of vectors

To show llinear depeneence and of independence of vectors

#### Unit 3 Bases and Dimensions

We will study about basis and dimension of vector spaces

#### Unit 3 Bases and Dimensions -2

continuation of bases and dimensions of vector spaces

#### UNIT3 Identical spaces

To study linear spaces

FAQ

FAQ

#### Assignment :Unit 3 Ass 4

Problems on linear combinations

#### Assignment:Unit 3 Ass 5

Problems on vector spaces

#### Assignment: unit 3 Ass 6

Problems on vector spaces

#### Assignment:Unit 3 Ass 7

Problems on vector spaces

Problems

Problems

Problems

#### UNIT4 Properties Of Linear Transformations

In this lecture ,we will discuss some special types of linear transformations .We will also examine some elementary properties of linear transformations.

#### UNIT4 The matrix of a linear transformation continued

In this lecture we will discuss the matrix representation of a linear transformation and will solve a few problems.

FAQ

Problems

#### Assignment UNIT4 Kernel and Image of a linear transformation

In this lecture, we will study two special subspaces associated with a linear transformation T: V → W, called the “kernel” and “range” of T. We will also illustrate techniques for calculating bases for both the kernel and range. We will see how dimensions of kernel and range are related to the dimension of the domain of a linear transformation.

#### UNIT4 Kernel and Image of a linear transformation continued

In this lecture we will discuss about the dimension theorem and will also solve some problems.

FAQ 2

Problems

#### Assignment Unit 4 Ass 4

Problems on linear Transformation

#### Assignment Unit 4 A3

Problems on linear Transformation

#### Assignment Unit 4 Ass 5

Problems on linear transformation

#### Assignment Unit 4 A5

Problems on linear transformation

#### Assignment:Unit 4 Ass 6

Problems on linear Transformation

Problems on LT

Problems on LT

Problems on LT

#### Assignment Unit 4 A9

Problems on Liner Transformation

#### Assignment UNIT 4 Linear Isomorphism

This topic will cover properties of isomorphism

FAQ 3

#### Assignment Unit 4 A 10

Problems on linear Transformation

Problems

Problems

Problems

FAQ 4

#### Unit 5 Lecture 31 Correlation and Regression, Rank Correlation – Module 1 & 2

Correlation and Regression, Rank Correlation.

#### Unit 5 Lecture 32 Method of least squares

Fitting a straight line, Parabola and higher degree curves

#### UNIT 6 Lecture 36

SIMPLE RANDOM SAMPLING

#### UNIT6 Lecture 37

HYPOTHESIS TESTING

#### UNIT6 Lecture 38

Test of significance for small samples

Chi-Square Test

#### Assignment:UNIT5 Correlation

To study the behaviour of two variables

FAQ

#### Assignment:UNIT 5 Rank Correlation

Problems related with rank correlation

FAQ 2

FAQ 3

#### Assignment:UNIT5 Curve fitting 1

To fit a curve of higher degree when data is given

#### Assignment :UNIT5 Curve Fitting 2

To fit exponential curve to given data

#### Assignment UNIT5 Probability Distribution-1

Problems on Binomial Distribution

#### Assignment: UNIT5 Probabllity Distribution-2

Problems on Poisson distribution

FAQ

#### Assignment UNIT5 Probability Distribution 3

Problems on Normal Distribution

FAQ

FAQ 2

#### Assignment unit 6 chi square

Problems on chi-square test

#### Assignment: unit 6 large sample

Problems on hypothesis testing

FAQ

#### Assignment:UNIT 6 Small Samples

Problems on hypothesis testing -small samples

#### Assignment:UNIT 6 Student-test

Problems on Students t-Test

FAQ

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### Seema Aggarwal

Assistant Professor

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### SAVITTA SAINI

Assistant Professor

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Level
All Levels
Duration 56 hours
Lectures
69 lectures
Subject
Language
English

#### Material Includes

• pdf notes

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