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    Linear Algebra: 40+ hours of Tutorials and Exercises!

    BY
    Udemy

    Develop a thorough understanding of the basic as well as advanced concepts related to linear algebra.

    Brochure Enquire
    Mode

    Online

    Fees

    ₹ 1999

    Quick Facts

    particular details
    Medium of instructions English
    Mode of learning Self study
    Mode of Delivery Video and Text Based

    Course overview

    Linear algebra is a branch of mathematics that deals with matrices, vectors as well as algebraic structures, and linear operations in general. Unlike other areas of mathematics, where innovative concepts and unresolved problems are occasionally stimulating, linear algebra is well comprehended. Linear Algebra: 40+ hours of Tutorials and Exercises certification course is created by Kvasir Education - Math Instructor, Bar Movsowowitz & Prop sA and is presented by Udemy. 

    Linear Algebra: 40+ hours of Tutorials and Exercises in online classes provide an elementary study of linear algebra that is appropriate for applicants with a science or mathematics background, to clearly understand the principles of linear algebra. Applicants who enroll in the Linear Algebra: 40+ Hours of Tutorials and Exercises online course will receive more than 48.5 hours of detailed lectures as well as 10 downloadable resources that explain concepts in linear algebra such as the system of linear equations, matrix, vector, matrix inverse, LU decomposition, determinant, adjoint matrix, eigenvectors, eigenvalues, product spaces, vector spaces, and more.

    The highlights

    • Certificate of completion
    • Self-paced course
    • 48.5 hours of pre-recorded video content
    • 10 downloadable resources

    Program offerings

    • Online course
    • Learning resources. 30-day money-back guarantee
    • Unlimited access
    • Accessible on mobile devices and tv

    Course and certificate fees

    Fees information
    ₹ 1,999
    certificate availability

    Yes

    certificate providing authority

    Udemy

    Who it is for

    Scientist

    What you will learn

    After completing the Linear Algebra: 40+ hours of Tutorials and Exercises online certification, applicants will be introduced to the foundational principles of linear algebra and the system of linear equations. Applicants will study concepts such as matrix, inverse matrix, adjoint matrix, LU decomposition, determinants, vector, vector spaces, and product spaces in mathematics. Applicants will get a better understanding of linear dependencies, linear independence, linear transformations, diagonalization, eigenvectors, and eigenvalues, as well as theories such as Cramer's rule and Markov chains.

    The syllabus

    1.1 Systems of Linear Equations

    • Systems of Linear Equations - What is a System of Linear Equations?
    • Solution of SLEs
    • Number of Solutions of an SLE
    • Row Echelon Form of an SLE
    • Solution of the Row Echelon Form
    • Transforming an SLE to Row Echelon Form
    • Solution of a General SLE
    • Using Matrices to Solve an SLE
    • Exercise 1
    • Exercise 2
    • Exercise 3
    • Exercise 4
    • Exercise 5
    • Exercise 6
    • Exercise 7
    • Exercise 8
    • Exercise 9
    • Exercise 10
    • Exercise 11
    • Exercise 12
    • Exercise 13
    • Exercise 14
    • Exercise 15
    • Exercise 16
    • Exercise 17 Part a
    • Exercise 17 Part b

    1.2 Systems of Linear Equations - SLE with Parameter

    • Row-Echelon Form with Parameter
    • Number of Solutions of SLE with Parameters I
    • Number of Solutions of SLE with Parameters II
    • Exercise 1
    • Exercise 2
    • Exercise 3
    • Exercise 4
    • Exercise 5
    • Exercise 6
    • Exercise 7
    • Exercise 8
    • Exercise 9
    • Exercise 10
    • Exercise 11
    • Exercise 12
    • Exercise 13 Parts a-c
    • Exercise 13 Parts d-f
    • Exercise 13 Parts g-h

    1.3 Systems of Linear Equations - SLE over Zp

    • Exercise 1
    • Exercise 2
    • Exercise 3
    • Exercise 4
    • Exercise 5
    • Exercise 6

    2.1 Matrices - Matrix and Basic Operations on Matrices

    • What is a Matrix?
    • What are the Special Matrices?
    • Times Scalar, Add & Subtract
    • Multiplication I
    • Multiplication II
    • Multiplication III
    • Transpose
    • Trace
    • Exercise 1
    • Exercise 2
    • Exercise 3 Parts 1-4
    • Exercise 3 Part 5
    • Exercise 3 Parts 6-7
    • Exercise 3 Part 8
    • Exercise 3 Part 9
    • Exercise 3 Part 10
    • Exercise 4
    • Exercise 5 Part 1
    • Exercise 5 Part 2
    • Exercise 5 Part 3
    • Exercise 5 Part 4
    • Exercise 5 Part 5
    • Exercise 6
    • Exercise 6 Part a
    • Exercise 6 Part b
    • Exercise 6 Part c
    • Exercise 6 Part d
    • Exercise 6 Part e

    Elementary Matrices and LU Decomposition

    • Elementary Matrices, Introduction
    • Elementary Matrices, Theorem
    • Exercise LU1
    • Exercise LU2

    2.2 Matrices - Matrix Inverse and its Applications

    • Inverse Matrix - Intro
    • How to Compute the Inverse Matrix
    • Using the Inverse Matrix to Solve an SLE
    • Exercise 1
    • Exercise 2
    • Exercise 3
    • Exercise 4
    • Exercise 5
    • Exercise 6
    • Exercise 7
    • Exercise 8
    • Exercise 9
    • Exercise 10
    • Exercise 11

    2.3 Matrices - Properties of the Matrix Inverse

    • Inverse Matrix - Rules
    • Exercise 1 Parts 1-3
    • Exercise 1 Parts 4-5
    • Exercise 1 Part 6
    • Exercise 2
    • Exercise 3
    • Exercise 4
    • Exercise 5
    • Exercise 6
    • Exercise 7
    • Exercise 8
    • Exercise 9

    3.1 Determinants - Introduction to Determinants

    • What is a Determinant?
    • Exercises 1-3
    • Exercises 4-6
    • Exercises 7-9
    • Exercise 10
    • Exercise 11

    3.2 Determinants - Rules of Determinants

    • Exercise 1 Parts 1-3
    • Exercise 1 Parts 4-6
    • Exercise 2
    • Exercise 3
    • Exercise 4
    • Exercise 5
    • Exercise 6
    • Exercise 7
    • Exercise 8
    • Exercise 9
    • Exercise 10
    • Exercise 11
    • Exercise 12
    • Exercise 13
    • Exercise 14
    • Exercise 15
    • Exercise 16
    • Exercise 17
    • Exercise 18
    • Exercise 19
    • Exercise 20

    3.3 Determinants - More Rules of Determinants

    • More Rules of Determinants
    • Exercise 1 Parts 1-2
    • Exercise 1 Parts 3-4
    • Exercise 2
    • Exercise 3
    • Exercise 4
    • Exercise 5
    • Exercise 6
    • Exercise 7
    • Exercise 8

    3.4 Determinants - Cramer's Rule

    • Cramer's Rule
    • Exercise 1
    • Exercise 2
    • Exercise 3
    • Exercise 4 Part a
    • Exercise 4 Part b
    • Exercise 4 Part c
    • Exercise 4 Part d

    3.5 Determinants - The Adjoint Matrix

    • The Adjoint Matrix - Intro
    • The Adjoint Matrix - Rules
    • Exercise 1
    • Exercise 2
    • Exercise 3
    • Exercise 4
    • Exercise 5 Part a
    • Exercise 5 Part b
    • Exercise 5 Part c
    • Exercise 5 Part d
    • Exercise 6

    3.6 Determinants - Geometrical Applications of Determinants

    • Exercise 1 Part a
    • Exercise 1 Part b
    • Exercise 1 Part c
    • Exercise 1 Part d

    4.1 Vector Spaces - The vector space Rn

    • Vector Subspaces
    • Vector Spaces - Part A
    • Vector Spaces - Part B
    • Vector Spaces - Part C
    • Exercise 1
    • Exercise 2
    • Exercise 3
    • Exercise 4
    • Exercise 5
    • Exercise 6
    • Exercise 7

    4.2 Vector Spaces - Linear Combinations and Span in R^n

    • Linear Combinations - Explanation & Example with 2 Solutions
    • The Linear Span
    • Linearly Dependent Vector
    • Exercise 1
    • Exercise 2
    • Exercise 3
    • Exercise 4
    • Exercise 5

    4.3 Vector Spaces - Linear Dependence in Rn

    • A Linearly Dependent Set of Vectors
    • Exercise 1
    • Exercise 2
    • Linear Dependence and Independence Set of Vectors
    • Proposition - A Sufficient Condition for Linear Independence

    4.4 Vector spaces - Basis For Rn

    • Basis of Rn
    • Exercise 1
    • Exercise 2
    • Exercise 3
    • Exercise 4

    4.5 Basis and Dimension for the Solution Space of a Homogeneous SLE in Rn

    • Basis and Dimension for the Solution Space of a Homogeneous SLE
    • Finding a Basis for the Solution Set of a Homogenous SLE
    • Exercise 1
    • Exercise 2
    • Exercise 3
    • Exercise 4
    • Exercise 5
    • Exercise 6
    • Exercise 7

    4.6 Vector Spaces - Basis of a Subspace of Rn

    • Basis for Subspace of Rn
    • Exercise 1 Part a
    • Exercise 1 Part b
    • Exercise 1 Part c
    • Exercise 1 Part d

    4.7 Vector Spaces - Basis for Row and Column Spaces

    • Row and Column Spaces
    • Exercise 1
    • Exercise 2

    4.8 Vector Spaces - Coordinate Vectors and Change of Basis in Rn

    • Coordinate Vectors
    • Change-of-Basis Matrix - Exercise 1 - Part 1
    • Change-of-Basis Matrix - Exercise 1 - Part 2
    • Change-of-Basis Matrix - Exercise 1 - Part 3
    • Change-of-Basis Matrix - Exercise 1 - Part 4
    • Change-of-Basis Matrix - Exercise 1 - Part 5

    4.9 Vector Spaces - Vector Spaces Beyond Rn

    • Review and more Vector Spaces over R
    • Vector Spaces over Fields other than R
    • Exercise 1
    • Exercise 2
    • Exercise 3
    • Exercise 4
    • Exercise 5
    • Exercise 6
    • Exercise 7
    • Exercise 8
    • Exercise 9
    • Exercise 10
    • Exercise 11
    • Exercise 12
    • Exercise 13
    • Exercise 14
    • Exercise 15
    • Exercise 16
    • Exercise 17
    • Exercise 18
    • Exercise 19
    • Exercise 20
    • Exercise 21
    • Exercise 22
    • Exercise 23
    • Exercise 24
    • Exercise 25

    4.10 Vector Spaces - Linear Combination - Advanced

    • Exercise 1 - Solution no.1
    • Exercise 1 - Solution no.2
    • Exercise 2 - Solution no.1
    • Exercise 2 - Solution no.2

    4.11 Vector spaces - Linear Dependence

    • Linear Dependence and Independence Set of Vectors
    • Example - Solution No.1
    • Example - Solution No.2
    • Proposition - A Sufficient Condition for Linear Dependence
    • Exercise 1
    • Exercise 2
    • Exercise 3
    • Exercise 4
    • Exercise 5
    • Exercise 6
    • Exercise 7
    • Exercise 8

    4.12 Vector spaces - Basis for Known Vector Spaces

    • Proposition - A Sufficient Condition for a Basis of a Famous Vector Space
    • Proposition - A Sufficient Condition for Not-a-Basis of a Famous Vector Space
    • The Dimension of Vector Spaces - Famous and General
    • The Standard Basis of Famous Vector Spaces
    • Exercise 1
    • Exercise 2

    4.13 Vector Spaces - Basis for a Solution Space, Homogeneous SLE

    • Exercise 1
    • Exercise 2
    • Exercise 3

    4.14 Vector Spaces - Coordinate Vectors and a Change of Basis

    • Coordinate Vectors - Relative to an Ordered Basis
    • How to Compute a Coordinate Vector Relative to a Given Basis
    • Example
    • Exercise 1 Part a
    • Exercise 1 Part b
    • Exercise 1 Part c
    • Exercise 2 Part a
    • Exercise 2 Part b
    • Exercise 2 Part c

    5.1 Eigenvectors, Eigenvalues and Diagonalization - Introduction

    • Eigenvectors and Eigenvalues - Introduction
    • Computing Eigenvalues and Eigenvectors
    • Algebraic and Geometric Multiplicity
    • Diagonalization of Matrices
    • Exercise 1 Parts a-f
    • Exercise 1 Parts i-j
    • Exercise 2 Parts a-f
    • Exercise 2 Parts i-j
    • Exercise 3 Parts a-f
    • Exercise 3 Parts g-h
    • Exercise 3 Parts i-j
    • Exercise 4 Parts a-f
    • Exercise 4 Parts g-h
    • Exercise 4 Parts i-j
    • Exercise 5
    • Exercise 5 - Shortcut
    • Exercise 6
    • Exercise 7
    • Exercise 8
    • Exercise 9
    • Exercise 10
    • Exercise 11
    • Exercise 12
    • Exercise 13
    • Exercise 14
    • Exercise 15
    • Exercise 16
    • Exercise 17
    • Exercise 18
    • Exercise 19
    • Exercise 20
    • Exercise 21
    • Exercise 22

    5.2 Eigenvectors Eigenvalues and Diagonalization - Matrix Similarity

    • Intro to Matrix Similarity and Exercise 1
    • Exercise 2
    • Exercise 3
    • Exercise 4
    • Exercise 5 - Parts a-c
    • Exercise 5 - Parts d-e
    • Exercise 5 - Parts f-g
    • Exercise 5 - Parts h-i

    6.1 Linear Transformation - Linear Transformation Definition

    • What is a Linear Transformation? Definition and Examples
    • Exercise 1
    • Exercise 2
    • Exercise 3
    • Exercise 4
    • Exercise 5
    • Exercise 6
    • Exercise 7
    • Exercise 8
    • Exercise 9
    • Exercise 10
    • Exercise 11
    • Exercise 12
    • Exercise 13
    • Exercise 14
    • Exercise 15
    • Exercise 16
    • Exercise 17
    • Exercise 18
    • Exercise 19
    • Exercise 20

    6.2 Linear Transformation - Image and Kernel

    • Kernel of a Linear Transformation
    • Image and Rank of a Linear Transformation
    • The Rank-Nullity Theorem (Dimension Theorem)
    • Exercise 1 Part a
    • Exercise 1 Part b
    • Exercise 2 Part a
    • Exercise 2 Part b
    • Exercise 3 Part a
    • Exercise 3 Part b
    • Exercise 4 Part a
    • Exercise 4 Part b
    • Exercise 5 Part a
    • Exercise 5 Part b
    • Exercise 6 Part a
    • Exercise 6 Part b
    • Exercise 7
    • Exercise 8
    • Exercise 9
    • Exercise 10

    6.3 Linear Transformations - Isomorphism and Inverse

    • Exercise 1 Part a
    • Exercise 1 Part b
    • Exercise 2
    • Exercise 3 Part a
    • Exercise 3 Part b
    • Exercise 4 Part a
    • Exercise 4 Part b

    6.4 Linear Transformations - Composition of Linear Transformation

    • Exercise 1
    • Exercise 2
    • Exercise 3
    • Exercise 4
    • Exercise 5
    • Exercise 6
    • Exercise 7
    • Exercise 8
    • Exercise 9

    7.1 Matrix of Linear Transformation - Reminder - Coordinate Vectors

    • Coordinate Vectors
    • Change-of-Basis Matrix - Exercise 1 - Part 1
    • Change-of-Basis Matrix - Exercise 1 - Part 2
    • Change-of-Basis Matrix - Exercise 1 - Part 3
    • Change-of-Basis Matrix - Exercise 1 - Part 4
    • Change-of-Basis Matrix - Exercise 1 - Part 5

    7.2 Matrix of Linear Transformation - Matrix of Linear Transformation

    • Exercise 1 - Part f
    • Exercise 1 - Part g
    • Exercise 1 - Part h
    • Exercise 1 - Part i
    • Exercise 1 - Part j
    • Exercise 2
    • Exercise 3
    • Exercise 4
    • Exercise 5
    • Exercise 6

    8.1 Inner Product Spaces

    • Lesson 1 - Intro - Inner Product & Inner Product Spaces
    • Lesson 2 - Formal Definition & Example 1
    • Lesson 3 - Example 2
    • The Conditions for Rn to be an Inner Product Space - Part 1
    • Part 2 and Worked Examples
    • Exercise 1
    • Exercise 2
    • Exercise 3
    • Exercise 4
    • Exercise 5
    • Exercise 6

    8.2 Inner Product Spaces - Norm and Distance

    • The Norm of a Vector in an IPS
    • Unit Vectors and Normalization of Vectors in IPS
    • Distance between Vectors in an IPS
    • Exercise 1
    • Exercise 2
    • Exercise 3
    • Exercise 4
    • Exercise 5
    • Exercise 6
    • Exercise 7
    • Exercise 8

    8.3 Inner Product Spaces - Cauchy–Schwarz Inequality

    • Cauchy–Schwarz Inequality
    • The Triangle Inequality
    • The Angle between Vectors
    • Exercise 1
    • Exercise 2
    • Exercise 3
    • Exercise 4
    • Exercise 5
    • Exercise 6
    • Exercise 7

    8.4 Inner Product Spaces - Orthogonality

    • Theory and Examples
    • Exercise 1
    • Exercise 2
    • Exercise 3
    • Exercise 4
    • Exercise 5
    • Exercise 6
    • Exercise 7
    • Exercise 8
    • Exercise 9

    8.5 Inner Product Spaces - Orthogonal Complement

    • The Orthogonal Complement of a Subspace
    • Exercise 1
    • Exercise 2
    • Exercise 3
    • Exercise 4
    • Exercise 5
    • Exercise 6
    • Exercise 7
    • Exercise 8
    • Exercise 9
    • Exercise 10
    • Exercise 11
    • Exercise 12
    • Exercise 13

    8.6 Inner Product Spaces - Orthogonal Sets and Bases

    • Orthogonal and Orthonormal Sets and Vectors
    • Orthogonal and Orthonormal Bases in an IPS
    • Exercise 1
    • Exercise 2
    • Exercise 3
    • Exercise 4
    • Exercise 5
    • Exercise 6
    • Exercise 7
    • Exercise 8
    • Exercise 9
    • Exercise 10

    9.1 Vectors - Introduction to 2D and 3D Vectors

    • Quantity with Magnitude and Direction - Part 1
    • Quantity with Magnitude and Direction - Part 2
    • Exercise 1

    9.2 Vectors - Vector Arithmetic

    • Explanation & Examples
    • Exercise 2
    • Exercise 3
    • Exercise 4
    • Exercise 5

    9.3 Vectors - Dot Product

    • Explanation & Examples - Part 1
    • Explanation & Examples - Part 2
    • Exercise 6
    • Exercise 7
    • Exercise 8
    • Exercise 9
    • Exercise 10

    9.4 Vectors - Cross Product

    • Vectors - Cross Product - Part 1
    • Vectors - Cross Product - Part 2
    • Exercise 11
    • Exercise 12
    • Exercise 13

    9.5 Vectors - The 3D Coordinate System

    • Explanation & Examples
    • Exercise 1
    • Exercise 2
    • Exercise 3
    • Exercise 4

    9.6 Vectors - Equations of Lines

    • The 3D Coordinate System - Equations of Lines - Part 1
    • The 3D Coordinate System - Equations of Lines - Part 2
    • Exercise 5
    • Exercise 6
    • Exercise 7
    • Exercise 8
    • Exercise 9
    • Exercise 10

    9.7 Vectors - Equations of Planes

    • The 3D Coordinate System - Equations of Planes - Part 1
    • The 3D Coordinate System - Equations of Planes - Part 2
    • Exercise 11
    • Exercise 12
    • Exercise 13
    • Exercise 14
    • Exercise 15
    • Exercise 16
    • Exercise 17
    • Exercise 18
    • Exercise 19

    9.8 Vectors - Quadric Surfaces

    • Explanation & Examples
    • Exercise 20
    • Exercise 21
    • Exercise 22
    • Exercise 23
    • Exercise 24

    10 Markov Chains

    • Explanation & Examples
    • Exercise 1 - Parts a-d
    • Exercise 1 - Part d - Continue
    • Exercise 2
    • Absorbing Markov Chains - Theory and Example

    Instructors

    Mr Amos Bahiri

    Mr Amos Bahiri
    Instructor
    Freelancer

    Other Bachelors, Other Masters

    Mr Bar Movsowowitz
    Instructor
    Freelancer

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