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    College Level Advanced Linear Algebra! Theory & Programming!

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    Udemy

    Develop a thorough understanding of the applications of linear algebra and calculus in areas such as machine learning, deep learning, and data science.

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    Online

    Fees

    ₹ 3099

    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 an area of application concerned with a system of equations and associated with vector space expressions via matrices. In other terms, one of the most important areas in mathematics is linear algebra, which is the analysis of linear functions and vectors. College Level Advanced Linear Algebra! Theory & Programming online certification is designed by Ahmed Fathy - MSc, Deep Learning Scientist & Instructor, and is delivered by Udemy.

    College Level Advanced Linear Algebra! Theory & Programming online course is intended for applicants who want to utilize calculus, linear algebra, and matrices for data science, machine learning, deep learning, computer graphics, and game development. College Level Advanced Linear Algebra! Theory & Programming online classes include 35 hours of digital lectures, 15 papers, and two downloadable resources on topics such as linear regression, principal component analysis, singular value decomposition, Taylor expansion, Hessian matrix, projection matrix, inverses, and pseudo inverses.

    The highlights

    • Certificate of completion
    • Self-paced course
    • 35 hours of pre-recorded video content
    • 15 articles 
    • 2 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
    ₹ 3,099
    certificate availability

    Yes

    certificate providing authority

    Udemy

    What you will learn

    After completing the College Level Advanced Linear Algebra! Theory & Programming certification course, applicants will gain a thorough understanding of linear algebra, calculus, and matrices to perform tasks such as deep learning, machine learning, data science, computer graphics, and control systems. Applicants will study the capabilities of programs such as Python and Matlab for various mathematical operations in programming. Applicants will learn about linear regression, singular value decomposition, and Taylor expansion, among other concepts. In addition, applicants will learn how to work with EigenVectors, EigenValues, normal equations, differential equations, inverses, pseudo inverses, Lagrange multipliers, Hessian matrix, and projection matrix.

    The syllabus

    Introduction To The Course

    • Welcome & Introduction!
    • Prerequisites
    • Exams, Written Scripts & Code Files

    Introduction To Matrices : Linear Independence And Matrix Multiplication

    • Column Method For Matrix Vector Multiplication
    • Linear Combinations And Independence - 1
    • Linear Combinations And Independence - 2
    • The Planes Picture Vs The Vectors Picture
    • Matrix Rank And Case Of Rectangular Matrices
    • Row By Matrix Multiplication
    • Matrix Matrix Multiplication - 1 - Dot Product Method
    • Matrix Matrix Multiplication - 2 - Column Method
    • Matrix Matrix Multiplication - 3 - Row Method
    • Matrix Matrix Multiplication - 4 - Outer Product
    • Matrix Matrix Multiplication - 5 - Block Multiplication

    Introduction To Gaussian Elimination And Matrix Inverse

    • Introduction To Gaussian Elimination
    • Gaussian Elimination With Row Exchange
    • Elimination Using Matrices
    • Row And Column Exchange Using Matrices
    • Intuition Of Matrix Inverse
    • Python Example & Matrix Inverse By Intuition
    • Gauss-Jordan Inverse With Proof
    • Python, Matlab & Hand Example For Matrix Inverse
    • Notes Regarding Inverses, Determinants, And Pseudo-Inverses

    Test Your Self ! - Exam 1!

    • Test Your Self ! - Exam 1!

    The Computer Graphics Section!

    • Introduction To Computer Graphics
    • The Computer Graphics Pipeline
    • Rotation By 90 Degrees Matrix In 2d
    • Rotation By Arbitrary Angle Matrix In 2d
    • Orthogonal Matrices And Their Inverses
    • Rotation About The X-Axis In 3d
    • The Scaling Matrix
    • The Homogeneous Coordinates And Translation Matrices
    • The Order Of Transformation Matters !
    • Reflection Matrix Around The X-Axis
    • Reflection Around Arbitrary Line In 2d - Method I
    • Reflection Around Arbitrary Line In 2d - Method Ii
    • Rotation About Arbitrary Axis In 3d - Method I
    • Rotation About Arbitrary Axis In 3d - Method Ii
    • Reflection Around Arbitrary Plane In 3d
    • Rotations & Improper Rotations
    • Notes About The Following Three Videos
    • Mathematics Of The Camera - I
    • Mathematics Of The Camera - Ii
    • Mathematics Of The Camera - Iii
    • Hierarchical Transformations And The Scene Graph

    The Robotics Section!

    • Robotics And Change Of Reference Frames - I
    • Robotics And Change Of Reference Frames Ii
    • Robotics And Change Of Reference Frames Iii
    • Matlab : Robotics And Change Of Reference Frames Iv - Numerical Example In 2d
    • Robotics And Change Of Reference Frames V - The 3d Situation
    • Robotics And Change Of Reference Frames Vi - The Camera Matrix Revisited

    Test Your Self ! - Exam 2!

    • Test Your Self ! - Exam 2!

    Test Your Self ! - Exam 3!

    • Test Your Self ! - Exam 3!

    Eigenvalues & Eigenvectors ( I ) : Introduction

    • Introduction To Eigenvalues And Eigenvectors
    • Eigenvs Geomteric Definition
    • Eigenvs - Intuitive Examples I
    • Eigenvs Intuitive Examples Ii
    • Eigenvs Formal Calculation
    • Eigenvs Numerical Examples - I
    • Eigenvs Numerical Examples - Ii
    • Repeated Eigenvalues And Dependent Eigenvectors
    • The Rotation Matrix And Complex Eigenvectors
    • Proof : Different Eigenvalues Have Independent Eigenvectors
    • Matrix Diagonalization Using Eigen Decomposition
    • Complex Eigenvs For Real Matrices Are Always Conjugate Pairs
    • Matrix Powers & Eigen Decomposition
    • Determinant Is The Product Of Eigenvalues

    Eigenvalues & Eigenvectors ( Ii ) : Difference Equations

    • Difference Equations & Eigen Decomposition
    • Matlab : Visualization Of Difference Equations Solved Example
    • Transforming Recurrence Relations To Matrix Form
    • The Case Of Complex Eigenvs & Difference Equations
    • Matlab : Visualization Of Complex Eigenvs And Difference Equations

    Eigenvalues & Eigenvectors ( Iii ) : Differential Equations

    • Systems Of Differential Equations
    • The Matrix Exponential And Its Diagonalization
    • Free Response Of A System Of Differential Equations - I
    • Free Response Of A System Of Differential Equations - Ii
    • Free Response Of A System Of Differential Equations - Iii
    • Free Response - Solved Example - I
    • Free Response - Solved Example - Ii
    • Matlab : Visualization Of Free Response Of Systems Of Differential Equations
    • Why Is It Called Free Response ?
    • Forced Response Of Systems Of Differential Equations
    • Forced Response - Solved Example
    • Matab : Visualization Of Forced Response Of Systems Of Differential Equations
    • Transforming Higher Order Odes To Systems Of First Order Odes

    Test Your Self ! - Exam 4!

    • Test Your Self ! - Exam 4!

    Matrix Inverse Using Cofactors & The Cayley Hamilton Theorem

    • The Cofactors Matrix And Adjoint Matrix
    • Proof : Matrix Inverse And Adjoint Matrix
    • The Cayley Hamilton Theorem - I
    • The Cayley Hamilton Theorem - Ii
    • The Cayley Hamilton Theorem - Iii
    • The Cayley Hamilton Theorem Iv
    • Matrix Exponential As A Finite Series

    Back To Systems Of Linear Equations ! - The Matrix Rank

    • Matrix Rank And Reduced Row Echelon Form - I
    • Matrix Rank And Reduced Row Echelon Form - Ii
    • Matrix Rank And Reduced Row Echelon Form Iii
    • Matrix Rank And Reduced Row Echelon Form Iv
    • Why Col Rank Equals Row Rank ? - I
    • Why Col Rank Equals Row Rank ? - Ii
    • Why Col Rank Equals Row Rank ? - Iii

    The Four Sub-Spaces Of A Matrix

    • The Column Space And The Row Space
    • Basis Of Column Space And Row Space
    • A More Simplified Basis For The Column Space
    • Gram-Shmidt Orhogonalization And Orthogonal Basis
    • Gram-Shmidt Orthogonalization Solved Example
    • The Null Space , What And Why ?
    • Getting The Null Space - I
    • Getting The Null Space - Ii
    • The Complete Solution To Ax=B For The Case Of Infinite Number Of Solutions
    • When Doesn't A Solution Exist ?
    • The Left Null Space Of A Matrix
    • The Relation Between The Four Sub-Spaces

    Solving The Unsolvable : Linear Regression, Projection Matrix & Normal Equation

    • The Projection Matrix & Normal Equation
    • The Nullspace Of Ata And The Uniqueness Of The Approximate Solution
    • The Case Of Infinite Number Of Approximate Solutions
    • The Projection Matrix
    • Linear Regression And Normal Equation
    • Linear Regression : Solved Example
    • Least Squares Error And The Normal Equation - Solved Example
    • Proof : Relation Between Least Squares Error And Normal Equation - I
    • Proof : Relation Between Least Squares Error And Normal Equation - Ii

    Test Your Self ! - Exam 5!

    • Test Your Self ! - Exam 5!

    A Section On Symmetric Matrices

    • The Eigen Decomposition Of Symmetric Matrices
    • The Norm Of A Complex Vector
    • Proof : Symmetric Matrices Have Real Eigenvalues
    • Proof: Symmetric Matrices With Distinct Eigenvalues Have Orthogonal Eigenvectors
    • Proof : Symmetric Matrices Have Orthogonal Eigenvectors - The Spectral Theorem
    • Proof: Shcur Triangulation Theorem
    • Space Elongation Direction & Eigen Decomposition Of Symmetric Matrices
    • Python : Visualization Of Data Maximum Spread Direction
    • More Geometric Intuition About Eigen Decomposition Of Symmetric Matrices

    A Section On Machine Learning And Data science

    • Intro To Data science And Machine Learning
    • Types Of Machine Learning
    • The Distance Similarity
    • Intuition Of Data Whitening
    • Mean, Variance, And Standard Deviation
    • Covariance - Intuition And Equation
    • The Covariance Matrix
    • The Covariance Matrix - Numerical Example
    • Mahalanobis Distance - The Simple Case
    • Condition For Data Whitening Transformation Matrices
    • The Mahalanobis Distance Derivation - The General Case

    Appendix A - The Lagrange Multipliers

    • About This Section
    • The Gradient Vector Is Perpendicular To The Surface
    • Gradient Vector In Higher Dimensions
    • Contour Lines
    • The Gradient Vector And Contour Lines
    • The Gradient Descent Algorithm
    • Introduction To Lagrange Multipliers - I
    • Matlab : Introduction To Lagrange Multipliers - Ii
    • Lagrange Multipliers - Solved Example
    • Lagrange Multipliers General Case Proof & Case With Multiple Constraints

    The Principal Component Analysis (Pca)

    • Introduction To The Pca
    • Pca Derivation - I
    • Pca Derivation - Ii
    • Pca Derivation - Iii
    • Pca Derivation Iv - Eigenvectors Of Covariance Matrix Are Principal Directions
    • Pca Derivation V - Eigenvalues Of Covariance Matrix Are The Variances
    • Pca Derivation Vi - The Second Principal Component
    • Pca Derivation Vii - Proof For Second & Third Principal Components
    • Pca - Covariance Between Principal Axis Is Zero
    • Pca Change Of Basis Matrix
    • Pca Dimensionality Reduction Matrix
    • Pca Data Whitening Matrix
    • Python Visualization : Pca Dimensionality Reduction & Whitening

    Test Your Self ! - Exam 6!

    • Test Your Self ! - Exam 6!

    The Singular Value Decomposition (Svd)

    • The Singular Value Decomposition - Introduction
    • Svd - The Geometric Picture - I
    • Svd - The Geomteric Picture - Ii
    • Svd - The Geomteric Picture - Iii
    • Svd - The Diagonalization Picture
    • Svd - The Four Spaces Picture
    • Svd - Revisiting The Geometric Picture
    • Svd - Geometric Intuition Of Svd Of Singular Matrices - 2d Example
    • Svd - Generalization For Square Matrices With Rank R
    • Svd - Generalization To Rectangular Matrices
    • Svd - The Calculation
    • Svd - The Nonzero Eigenvalues Of Ata & Aat
    • Matlab And Pen : Svd Numerical Example - Square Matrix
    • Matlab And Pen : Svd Numerical Example - Rectangular Matrix - I
    • Matlab And Pen : Svd Numerical Example - Rectangular Matrix - Ii
    • Svd For Data Compression
    • Matlab : Svd & Image Compression
    • Matlab : Svd And Pattern Extraction - I
    • Matlab : Svd And Pattern Extraction - Ii
    • The Relation Between The Svd And The Pca

    The Pseudo Inverse Of A Matrix

    • Pseudo Inverse Introduction And Intuition - I
    • Pseudo Inverse Introduction And Intuition Ii
    • Pseudo Inverse Introduction And Intuition Iii
    • The Pseudo Inverse Derivation - I
    • The Pseudo Inverse Derivation - Ii
    • More Intuition About A * A_plus & A_plus * A
    • Another Derivation Of The Pseudo Inverse
    • The Left & Right Inverses Of A Matrix
    • The Pseudo Inverse And Infinite Number Of Least Squares Error Solutions

    Test Your Self ! - Exam 7!

    • Test Your Self ! - Exam 7!

    The Lu Decomposition

    • Introduction To Lu Decomposition Of A Matrix
    • More Insights Into The L Matrix - I
    • More Insights Into The L Matrix - Ii
    • Ldu & Ldl_t Decompositions
    • Lup Decomposition & The Principal Minors
    • Lu Decomposition In Practice

    A Video On Positive Definite Matrices - Will Come Back In A Subsequent Section!

    • Introduction To Positive Definite Matrices

    Appendix B : The Taylor Expansion

    • Taylor Expansion In 1d
    • The Directional Derivative
    • Taylor Expansion In Higher Dimensions
    • Second Order Taylor Expansion And The Hessian Matrix
    • Min Max Tests In One Dimension
    • Min Max Tests In Higher Dimensions & The Hessian Matrix

    Back To Positive Definite Matrices !

    • Why Care About Properties Of Positive Definite Matrices ?
    • Positive Definiteness Means Positive Eigenvalues And Vice-Versa
    • Important Notes About The Hessian Matrix And Its Eigenvectors
    • Positive Definite Matrices Always Have Ldl_t Decomposition
    • Positive Definite Matrices Always Have Positive Pivots
    • Introduction To Quadratic Forms
    • Quadratic Forms And Symmetric Matrices
    • Positive Definite Matrices And Ellipsoids - I
    • Positive Definite Matrices And Ellipsoids - Ii
    • Positive Definite Matrices And Ellipsoids - Iii
    • Positive Definite Matrices And Ellipsoids - Vi
    • Shifting The Center Of The Ellipse
    • Relation Between Completing The Squares And Matrix Pivots
    • Choleskly Decomposition And Positive Definite Matrices
    • Covariance Matrix And Ata Are Always Positive Semidefinite

    Determinants!

    • Introduction To Determinants
    • Intuition Of Determinants
    • The Three Primary Properties That Define The Determinant
    • Determinant Using Gaussian Elimination - Solved Example
    • Sign Of The Determinant Intuition And Effect Of Exchanging Rows
    • Determinant Of Singular Matrices Is Zero
    • Determinant Of Diagonal And Triangular Matrices
    • The Linear Property Of Determinants
    • Determinant Of (Ab) - Geometeric Picture Proof
    • Singularity Of (Ab) When Either A Or B Is Singular
    • Det(Ab) = Det(A) * Det(B) Formal Proof
    • Proof : Inverse Of A Permutation Matrix Is Its Transpose
    • Proof : Det (A_t) = Det(A)
    • Geometric Intuition Of Determinant As Product Of Eigenvalues
    • Determinant Of Orthogonal Matrices
    • Determinant Of Matrix Inverse
    • The Cofactor (Laplace Expansion) : Statement
    • The Cofactor Expansion - Solved Example
    • The Cofactor Expansion Proof - I
    • The Cofactor Expansion Proof - Ii
    • The Cofactors Expansion Proof - Iii
    • The Cofactors Expansion Proof - Vi
    • Cramer's Rule For Solving Systems Of Linear Equations

    Matrix Calculus - I : The Basics

    • Introduction To Matrix Calculus
    • Differentiation Of A Vector Wrt A Scalar
    • Differentiation Of A Scalar Wrt A Vector
    • The Jacobian And Differentiation Of A Vector Wrt A Vector
    • Differentiation Of A Matrix Wrt A Scalar
    • Differentiation Of A Scalar Wrt A Matrix
    • Differentiation Of A Vector Wrt A Matrix
    • Derivative Of A Matrix Wrt A Matrix
    • The Chain Rule For Vector Wrt Vector Differentiation
    • Chain Rule & Matrix Tensor Multiplication

    Matrix Calculus Ii : On The Relation Between The Jacobian And Double Integrals

    • About This Section
    • Introduction
    • Quick Review On The Fundamental Theorem Of Calculus
    • Quick Review On Variable Substitution In 1d Integrals
    • Deeper Geometric Intuition Of Variable Substitution In 1d Integrals - I
    • Deeper Geometric Intuition Of Variable Substitution In 1d Integrals - Ii
    • Quick Review On Double Integrals
    • Another Way To Look At Double Integrals
    • Variable Substitution In Double Integrals - I
    • Variable Substitution In Double Integrals - Ii
    • Variable Substitution In Double Integrals - Iii
    • The Jacobian Determinant And Double Integrals
    • The Jacobian Determinant And Double Integrals : Solved Example

    Matrix Calculus - Iii : More On Matrix Calculus

    • Product Differentiation Rules For Matrices
    • Derivative Of Product Of Two Scalar Functions Of A Matrix
    • Derivative Of Product Of Two Matrix Functions Of A Scalar
    • Derivative Of Dot Product Of Two Vectors With Respect To A Third Vector
    • Derivative Of Ax With Respect To X
    • Derivative Of Ax With Respect To Z
    • Derivative Of Quadratic Form Yt * A * X With Respect To Y & X
    • Derivative Of Quadratic Form Xt * A * X With Respect To X
    • The Linear Regression Equation Revisited
    • Derivative Of Matrix Inverse With Respect To A Scalar
    • Derivative Of Quadratic Form Yt * A * X With Respect To A
    • Derivative Of Matrix Determinant With Respect To A Scalar - I
    • Derivative Of Matrix Determinant With Respect To A Scalar - Ii
    • Derivative Of Matrix Determinant With Respect To The Matrix Itself
    • Quick Review On Maximum Likelihood Estimation
    • Maximum Likelihood Estimation Of Single Variable Gaussian Distribution
    • Maximum Likelihood Estimation Of Multi-Variate Gaussian Distribution - I
    • Maximum Likelihood Estimation Of Multi-Variate Gaussian Distribution - Ii

    Test Your Self ! - The Final Exam!

    • Test Your Self ! - The Final Exam!

    Extra - I :: Homogeneous Coordinates And The Projection Matrix Derivation !

    • About This Section
    • An Overview Of Homogeneous Coordinates
    • The Intuition Of Perspective Projection
    • Derivation Of Perspective Projection Matrix - Part 1
    • Derivation Of Perspective Projection Matrix - Part 2
    • Perspective Projection Code In Glmatrix Library [Javascript]

    Bonus : Get My Other Courses!

    • Get My Other Courses!

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