 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

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

Material Includes

• pdf notes

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