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# Linear Algebra Basics

### Overview

Class Central Tips
Machine learning and data science are the most popular topics of research nowadays. They are applied in all the areas of engineering and sciences. Various machine learning tools provide a data-driven solution to various real-life problems. Basic knowledge of linear algebra is necessary to develop new algorithms for machine learning and data science. In this course, you will learn about the mathematical concepts related to linear algebra, which include vector spaces, subspaces, linear span, basis, and dimension. It also covers linear transformation, rank and nullity of a linear transformation, eigenvalues, eigenvectors, and diagonalization of matrices. The concepts of singular value decomposition, inner product space, and norm of vectors and matrices further enrich the course contents.

### Syllabus

• Getting Started with the Course
• This module provides an overview of the course content and structure. In this module, you will learn about the different course elements. In this module, you will get acquainted with your instructor and get an opportunity to introduce yourself and interact with your peers.
• Vector Space
• In this module, you will learn about vector space and its subspace. Further, you will learn about the set of linearly dependent and independent vectors. You will also gain insight into the linear combination and linear span of a set of vectors.
• Linear Transformations and Eigenvalues
• In this module, you will learn about the basis and dimension of a vector space. You will learn about the concept of linear transformations defined on real vector spaces. Further, you will understand that there is a matrix associated with each linear transformation for the bases. Finally, you will get an insight into the eigenvalues of a square matrix.
• Diagonalizable Matrices and Their Applications
• In this module, you will learn about the eigenvectors corresponding to the eigenvalues of a matrix. You will then learn about the properties of special matrices (symmetric and skew-symmetric). Finally, you will learn about the concept of diagonalization of a matrix (eigen decomposition of a matrix) with its applications.
• Singular Value Decomposition of a Matrix and Inner Product of Vectors
• In this module, you will learn about the spectral value decomposition and singular value decomposition of a matrix with some applications. Further, you will learn about the inner product space and norms of vectors and matrices with two useful identitiesâ€”Cauchy-Schwarz inequality and Polarization identityâ€”for machine learning algorithms.
• Term-End Assignment
• In this module, you are provided with your term-end project, instructions to complete the project, and the criteria for how your instructor will grade your submission.

Dr. S. K. Gupta

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