# Linear Algebra & Statistical Techniques

#### About This Course

**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

#### Target Audience

- All Students

#### Curriculum

69 Lessons56h

#### Unit -I Introduction to Matrices Module-I

##### Lesson 1 Module-100:00:00

##### Assignment_introduction to matrices

##### Introduction to Matrices

#### 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.

#### UNIT1 Rank of Matrix Module -II

#### : 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.

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

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 .

#### Unit 1 FAQ

FAQs

#### Unit ! FAQ

FAQ

#### Unit 1FAQ

FAQ

#### FAQ Unit 1

FAQ

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

#### UNIT 2 Homogeneous Linear Systems (Rank)Module-II

#### 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 Non Homogeneous Linear Systems(Rank) Module -II

#### 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 Cayley Hamilton theorem-module 2

#### 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.

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

#### FAQ Unit 2

FAQ

#### FAQ-Unit 2

Faq on unit 2

#### FAQ Unit 2

FAQ

#### FAQ Unit 2

FAQ

#### UNIT3 Lesson 11

#### Unit 3 Vector Spaces module I & II

#### 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

#### FAQ UNIT 3

Frequently Asked Questions 1

#### Unit 3 Linear Independece of vectors

To study about linear independence and linear depence of vectors

#### FAQ Unit 3

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

#### Linear Space

To Study about linear Spaces

#### FAQ Unit 3

FAQ

#### FAQ Unit 3

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

#### Assignment: Unit 3 Bases and Dimensions 2

Problems

#### Assignment :Unit 3 linear combination

#### Assignment Unit 3 Lesson 12

Problems

#### Assignment Unit 3 L 16

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 Unit 4

FAQ

#### Linear operator and similarity

#### Assignment UNIT4 Linear Transformation

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.

#### UNIT 4 L-28

#### FAQ Unit 4

FAQ 2

#### UNIT4 Lecture 30 Isomorphic spaces

To study about isomorphic spaces

#### UNIT 4 L-29

#### UNIT4 Linear Algebra Ass 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

#### Assignment Unit 4 A ss 7

Problems on LT

#### Assignment Unit 4 A7

Problems on LT

#### Assignment Unit 4 A8

Problems on LT

#### Assignment Unit 4 A9

Problems on Liner Transformation

#### Assignment UNIT 4 Linear Isomorphism

This topic will cover properties of isomorphism

#### FAQ Unit 4

FAQ 3

#### Assignment Unit 4 A 10

Problems on linear Transformation

#### Assignment :UNIT4Linear Algebra Ass 1

Problems

#### Assignment :UNIT4Linear algebra Ass 3

Problems

#### Assignment :Unit 4 L24

Problems

#### FAQ Unit 4

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

#### UNIT6 Lecture 40

Chi-Square Test

#### Assignment:UNIT5 Correlation

To study the behaviour of two variables

#### FAQ Unit 5

FAQ

#### Assignment:UNIT 5 Rank Correlation

Problems related with rank correlation

#### FAQ Unit 5

FAQ 2

#### FAQ Unit 5

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 Unit 5

FAQ

#### Assignment UNIT5 Probability Distribution 3

Problems on Normal Distribution

#### FAQ Unit 6

FAQ

#### FAQ Unit 6

FAQ 2

#### Assignment unit 6 chi square

Problems on chi-square test

#### Assignment: unit 6 large sample

Problems on hypothesis testing

#### FAQ Unit 6

FAQ

#### Assignment:UNIT 6 Small Samples

Problems on hypothesis testing -small samples

#### Assignment:UNIT 6 Student-test

Problems on Students t-Test

#### FAQ Unit 6

FAQ