Overview

Short Summary about the need and importance of the CourseLinear Algebra is the backbone of Data Science, Machine Learning (ML), and Artificial Intelligence (AI). Understanding its core concepts is essential to grasp the functionality of ML algorithms. However, most courses make this process overwhelming by focusing on complex calculations rather than the practical application you need to understand the working of Machine Learning Algorithms. How our course is different ?We've designed this Linear Algebra course specifically for aspiring Data Scientists and Machine Learning enthusiasts who want to dive into the essentials without wasting time. In just around 7.5 hours, you'll master the key concepts required for Machine Learning, with a clear focus on how these concepts apply directly to real-world Machine Learning algorithms. This Course will teach you the geometric intuition and essential computations so that you can think like a Machine Learning Expert.Please find the Complete Syllabus for the Course belowMathematics for Machine Learning: 1. Introduction to linear AlgebraDifference 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.Mathematics for Machine Learning: 2. Geometric representation of an expressionGeometric visualization of an algebraic expression with an example, Gradient of a straight line, Generalization of an expression geometrically on an N dimensional plane.Mathematics for Machine Learning: 3. Importance of a System of linear EquationDefinition 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.Mathematics for Machine Learning: 4. Vector representation of a System of linear equationsNeed 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.Mathematics for Machine Learning: 5. Introduction to Vectors for Machine LearningScalar, 2-D and 3-D data representation of vectors geometrically, generalization of N-D data into N-dimensional plane.Mathematics for Machine Learning: 6. Vector: Magnitude and DirectionDifferent 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.Mathematics for Machine Learning: 7. Application of Magnitude of a VectorDistance between vectors in a 2-D plane and its generalization onto N-D plane, Euclidian distance between two vectors.Mathematics for Machine Learning: 8. Position and Displacement VectorRepresenting 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.Mathematics for Machine Learning: 9. Addition, Subtraction and Scaling of a VectorExplanation of Geometric Visualization of Addition, Subtraction and Scaling of two vectors.Mathematics for Machine Learning: 10. Dot Product between two vectorsTypes 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.Mathematics for Machine Learning: 11. Projection of a VectorExplanation 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.Mathematics for Machine Learning: 12. Application of Projection of a VectorUnderstanding the need for projection of a Vector while solving a Machine Learning problem with an Example.Mathematics for Machine Learning: 13. Vector Spaces and SubspacesDefinition 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.Mathematics for Machine Learning: 14. Feature space and Input feature vectorGeometric 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.Mathematics for Machine Learning: 15. Span of VectorsMathematical 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.Mathematics for Machine Learning: 16. Linear Independence of vectorsMathematical definition of linear Independence of vectors, linear combination of vectors, determining linearly independent vectors.Mathematics for Machine Learning: 17. Application of linearly independent vectorsSolving a classification and a regression Machine learning problem using linearly independent vectors, property of dimension of a decision boundary.Mathematics for Machine Learning: 18. Basis of a SubspaceChoosing vectors to form the basis, Definition of basis of a subspace, Dimension of a subspaceMathematics for Machine Learning: 19. Gaussian EliminationBasis of a Vector Space, Finding the basis and dimension of Vectors using Gaussian Elimination, Row Echelon form of a Matrix, Rank of a Matrix.Mathematics for Machine Learning: 20. Gaussian Elimination ApplicationSolving system of Linear Equations using Gaussian Elimination, Augmented Matrix, Reduced Row Echelon form and its properties.Mathematics for Machine Learning: 21. Orthogonal BasisOrthogonal Set, Orthogonal Vectors, Orthogonal Basis and its definition, formula to represent any vector in terms of Basis vectors with an Example.Mathematics for Machine Learning: 22. Orthonormal BasisOrthonormal Set, Orthonormal Vectors, Orthonormal Basis, and its definition.Mathematics for Machine Learning: 23. Gram-Schmidt OrthogonalizationNeed for Orthogonalization, Gram-Schmidt Orthogonalization procedure, Determining Orthogonal and Orthonormal Basis using Gram-Schmidt method.Mathematics for Machine Learning: 24. Span VisualizationSpan 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.Mathematics for Machine Learning: 25. Linear TransformationDefinition of Linear Transformation, Domain and Codomain, Properties of linear transformation with examples, Matrix Vector multiplication.Mathematics for Machine Learning: 26. Kernel and ImageKernel and its Definition, Image and its Definition, Attributes of linear transformation.Mathematics for Machine Learning: 27. Application of Linear TransformationAX=b as a function, projecting a vector from higher dimensional space onto a lesser dimensional space using linear transformation.Mathematics for Machine Learning: 28. Application of Linear Transformation in MLMethods of linear transformation, Normalization and Standardization of features, Demonstration of Normalization and Standardization using a Python code, Non-linear Transformation.Mathematics for Machine Learning: 29. Types of Matrix and Matrix EquationsTypes 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.Mathematics for Machine Learning: 30. Determinant and its ApplicationDefinition 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.Mathematics for Machine Learning: 31. Inverse of a MatrixDefinition of Inverse of a matrix, Invertible and Non-Invertible matrix with an example.Mathematics for Machine Learning: 32. Determinants IIDemonstration of five applications of Determinant of a matrix using a Python Code.Mathematics for Machine Learning: 33. Inverse of a Matrix IIApplication 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.Mathematics for Machine Learning: 34. Eigen vector and Eigen valueDefinition 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.Mathematics for Machine Learning: 35. Similar Matrix and Similarity transformationTransformation matrix, Similar matrix, Similarity Transformation, Similarity matrix, Properties of Similar matrix.Mathematics for Machine Learning: 36. Diagonalization of a MatrixDerivation 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.Mathematics for Machine Learning: 37. Eigen DecompositionDefinition and derivation of Eigen decomposition of a matrix, Rules to perform eigen decomposition, Algebraic and geometric multiplicity, Application of Eigen decomposition in Machine Learning.Mathematics for Machine Learning: 38. Orthogonal MatrixDefinition of Orthogonal matrix, Properties of Orthogonal Matrix, Demonstration of properties of an Orthogonal matrix using a Python code.Mathematics for Machine Learning: 39. Symmetric MatrixDefinition of Symmetric matrix, Properties of Symmetric matrix.Mathematics for Machine Learning: 40. Singular Value DecompositionDefinition 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.Hurry!!! with no Worry and get enrolled today!! as Udemy provides you with a 30 day money back guarantee if you don't like the Course.Get started today Happy Learning!!!

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