Linear Algebra for Machine Learning, Data Science & AI 2024

Welcome to the comprehensive course on Linear Algebra for Machine Learning. This Machine Learning course is your gateway to mastering the essential tools needed for Machine Learning. Designed specifically for Machine Learning students, Machine Learning Engineers, and those pursuing a Masters in Machine Learning, this course focuses on practical, algorithmic applications within Machine Learning. We go beyond theory to show you how Linear Algebra powers the algorithms and techniques that drive Machine Learning. This isn’t for pure Math students; it’s for those who want to harness the power of Linear Algebra to solve real-world Machine Learning problems and advance their careers. Join us and gain the skills to excel in the dynamic world of Machine Learning.

Linear Algebra for Machine Learning is an essential foundation for understanding the mechanics behind many Machine Learning algorithms. From data preprocessing to model optimization, the principles of Linear Algebra are woven into every aspect of Machine Learning. This course will guide you through these principles with a clear emphasis on their relevance and application to Machine Learning.

For Machine Learning students, grasping the concepts of Linear Algebra is crucial for success. The course content includes matrix operations, vector spaces, and eigenvalues, all framed within the context of Machine Learning problems. Understanding Linear Algebra will enable you to comprehend complex Machine Learning models and improve your ability to implement Machine Learning algorithms effectively.

Machine Learning Engineers will find this course invaluable for optimizing their Machine Learning models and solving computational problems. Linear Algebra provides the tools needed to handle large datasets efficiently and to perform operations such as dimensionality reduction and data transformation. By mastering Linear Algebra, Machine Learning Engineers can enhance the performance and accuracy of their Machine Learning algorithms.

For those pursuing a Masters in Machine Learning, this course offers an in-depth exploration of Linear Algebra. Advanced topics such as dimensionality reduction and Singular Value Decomposition (SVD) will be covered extensively, showcasing their applications in Machine Learning. This knowledge is critical for research and development in multifarious fields, making Linear Algebra a cornerstone of advanced Machine Learning studies.

In summary, this course on Linear Algebra for Machine Learning is designed specifically for individuals who aim to apply mathematical concepts to Machine Learning, rather than for pure Math students. By focusing on practical applications and real-world examples, we ensure that you gain the skills necessary to excel in the dynamic field of Machine Learning.

Please find the Syllabus for the Course below

Linear Algebra for Machine Learning: 1. Introduction to linear Algebra
Difference between Algebra and Linear Algebra, Definition of Linear Algebra, Linear Equation and System of linear equations with an Example, Attributes and properties of system of linear equation.

Linear Algebra for Machine Learning: 2. Geometric representation of an expression
Geometric visualization of an algebraic expression with an example, Gradient of a straight line, Generalization of an expression geometrically on an N dimensional plane.

Linear Algebra for Machine Learning: 3. Importance of a System of linear Equation
Definition and Goal of System of Linear Equations, General form of system of Linear Equations, representing a dataset in terms of System of linear equations, Applications of system of linear equations in solving a classification and a regression problem with an example of a dataset.

Linear Algebra for Machine Learning: 4. Vector representation of a System of linear equations
Need for vector representation of a system of linear equations while solving a Machine Learning problem, Properties, and advantages of vector representation of a system of linear equations.

Linear Algebra for Machine Learning: 5. Introduction to Vectors for Machine Learning
Scalar, 2-D and 3-D data representation of vectors geometrically, generalization of N-D data into N-dimensional plane.

Linear Algebra for Machine Learning: 6. Vector: Magnitude and Direction
Different types of representation of a Vector, Component form, Row & Column Vector form, Determining the magnitude of a vector, determining direction of a vector using Unit vector.

Linear Algebra for Machine Learning: 7. Application of Magnitude of a Vector
Distance between vectors in a 2-D plane and its generalization onto N-D plane, Euclidian distance between two vectors.

Linear Algebra for Machine Learning: 8. Position and Displacement Vector
Representing the position of a Point, line and a plane using position vector geometrically, Introduction to an Online tool to visualize a vector geometrically, Visualization of a displacement vector with an example.

Linear Algebra for Machine Learning: 9. Addition, Subtraction and Scaling of a Vector
Explanation of Geometric Visualization of Addition, Subtraction and Scaling of two vectors.

Linear Algebra for Machine Learning: 10. Dot Product between two vectors
Types of Vector Multiplications, Need for Dot product between two vectors, Two forms of Dot product, Determining Similarity and Dissimilarity of two vectors using dot product, Difference between component form and polar form of a dot product, Application of dot product between vectors with an example.

Linear Algebra for Machine Learning: 11. Projection of a Vector
Explanation of projection of a Vector, Two types of projection of a Vector, Deriving formula of types of projection of Vectors, Difference between Scalar and Vector projection.

Linear Algebra for Machine Learning: 12. Application of Projection of a Vector
Understanding the need for projection of a Vector while solving a Machine Learning problem with an Example.

Linear Algebra for Machine Learning: 13. Vector Spaces and Subspaces
Definition of Mathematical Structure, Definition of Vector Space, Mathematical definition of Vector Space, Example of a vector space, Mathematical definition of Subspace along with an example.

Linear Algebra for Machine Learning: 14. Feature space and Input feature vector
Geometric visualization of a feature space and Input feature vector, Assumptions of vector space, Simple Application of Vector Addition and Multiplication on a feature space, Mean of a Vector, Linear transformation of a Vector.

Linear Algebra for Machine Learning: 15. Span of Vectors
Mathematical and theoretical definition of Span of Vectors, Geometric intuition of Span of a Vector, Example of Span of a Vector, Geometric intuition and mathematical definition of span of two vectors, dependent and independent vectors, Span of dependent and independent vector.

Linear Algebra for Machine Learning: 16. Linear Independence of vectors
Mathematical definition of linear Independence of vectors, linear combination of vectors, determining linearly independent vectors.

Linear Algebra for Machine Learning: 17. Application of linearly independent vectors
Solving a classification and a regression Machine learning problem using linearly independent vectors, property of dimension of a decision boundary.

Linear Algebra for Machine Learning: 18. Basis of a Subspace
Choosing vectors to form the basis, Definition of basis of a subspace, Dimension of a subspace

Linear Algebra for Machine Learning: 19. Gaussian Elimination
Basis of a Vector Space, Finding the basis and dimension of Vectors using Gaussian Elimination, Row Echelon form of a Matrix, Rank of a Matrix.

Linear Algebra for Machine Learning: 20. Gaussian Elimination Application
Solving system of Linear Equations using Gaussian Elimination, Augmented Matrix, Reduced Row Echelon form and its properties.

Linear Algebra for Machine Learning: 21. Orthogonal Basis
Orthogonal Set, Orthogonal Vectors, Orthogonal Basis and its definition, formula to represent any vector in terms of Basis vectors with an Example.

Linear Algebra for Machine Learning: 22. Orthonormal Basis
Orthonormal Set, Orthonormal Vectors, Orthonormal Basis, and its definition.

Linear Algebra for Machine Learning: 23. Gram-Schmidt Orthogonalization
Need for Orthogonalization, Gram-Schmidt Orthogonalization procedure, Determining Orthogonal and Orthonormal Basis using Gram-Schmidt method.

Linear Algebra for Machine Learning: 24. Span Visualization
Span of a Vector on 2-D space, Span of 2 Vectors on a 2-D space, Span of a vector on a 3-D space, Span of 2 vectors on a 3-D space, Span of 3 Vectors on a 3-D space.

Linear Algebra for Machine Learning: 25. Linear Transformation
Definition of Linear Transformation, Domain and Codomain, Properties of linear transformation with examples, Matrix Vector multiplication.

Linear Algebra for Machine Learning: 26. Kernel and Image
Kernel and its Definition, Image and its Definition, Attributes of linear transformation.

Linear Algebra for Machine Learning: 27. Application of Linear Transformation
AX=b as a function, projecting a vector from higher dimensional space onto a lesser dimensional space using linear transformation.

Linear Algebra for Machine Learning: 28. Application of Linear Transformation in ML
Methods of linear transformation, Normalization and Standardization of features, Demonstration of Normalization and Standardization using a Python code, Non-linear Transformation.

Linear Algebra for Machine Learning: 29. Types of Matrix and Matrix Equations
Types of Matrix for solving ML problems, Types of Matrix equations, Homogeneous equation and its properties, Non Homogeneous equation and its properties, Consistent and Inconsistent solution, Example of Non trivial solution AX=0.

Linear Algebra for Machine Learning: 30. Determinant and its Application
Definition of Determinant, determining the determinant of a matrix, Singular and Non-Singular matrix, Matrix transformation and its properties, five different applications of determinants in ML.

Linear Algebra for Machine Learning: 31. Inverse of a Matrix
Definition of Inverse of a matrix, Invertible and Non-Invertible matrix with an example.

Linear Algebra for Machine Learning: 32. Determinants II
Demonstration of five applications of Determinant of a matrix using a Python Code.

Linear Algebra for Machine Learning: 33. Inverse of a Matrix II
Application of Inverse of a matrix in Machine Learning, Rules for invertibility of matrix, Hurdles to determine the invertibility of a matrix in Machine Learning, Methods to overcome the hurdles.

Linear Algebra for Machine Learning: 34. Eigen vector and Eigen value
Definition of Eigen vector and Eigen value, Example of Eigen vector, Procedure to calculate Eigen vector and Eigen value, Determining Eigen Vector and Eigen Value using a Python Code.

Linear Algebra for Machine Learning: 35. Similar Matrix and Similarity transformation
Transformation matrix, Similar matrix, Similarity Transformation, Similarity matrix, Properties of Similar matrix.

Linear Algebra for Machine Learning: 36. Diagonalization of a Matrix
Derivation of formula for Diagonalization of a Matrix, Geometric intuition of Diagonalization of a Matrix, Definition of Diagonalization of a matrix, Application of diagonalization of a matrix in Machine Learning.

Linear Algebra for Machine Learning: 37. Eigen Decomposition
Definition and derivation of Eigen decomposition of a matrix, Rules to perform eigen decomposition, Algebraic and geometric multiplicity, Application of Eigen decomposition in Machine Learning.

Linear Algebra for Machine Learning: 38. Orthogonal Matrix
Definition of Orthogonal matrix, Properties of Orthogonal Matrix, Demonstration of properties of an Orthogonal matrix using a Python code.

Linear Algebra for Machine Learning: 39. Symmetric Matrix
Definition of Symmetric matrix, Properties of Symmetric matrix.

Linear Algebra for Machine Learning: 40. Singular Value Decomposition
Definition of Singular value decomposition, Derivation of SVD along with its geometric intuition, Determining the matrices to perform SVD, Properties of SVD, Application of SVD in Machine Learning.

Please Note: This course is not designed for Math graduates learning Linear Algebra, instead it is designed for Machine Learning and Artificial Intelligence aspirants, who can quickly grasp the essential fundamentals of linear algebra before diving deep into Machine Learning Concepts. 

Happy Learning!!!

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