Do you want to learn how to work with abstract spaces and transformations that preserve their structure? Do you want to understand the concepts of vector subspaces, linear combinations, linear dependence, basis, dimension, coordinates, and properties of vector spaces? Do you want to master the skills of defining and manipulating linear maps, their kernels, images, matrix representations, and transition matrices? If you answered yes to any of these questions, then this course is for you! Linear Algebra: Linear Vector Spaces and Linear Maps is a comprehensive and engaging course that covers the fundamentals of vector spaces and linear maps and their applications in mathematics and science. You will learn how to: - Define and classify vector spaces and their subspaces over a given scalar field - Perform operations on vectors using linear combinations and scalar multiplication - Determine whether a set of vectors is linearly dependent or independent and find a basis and dimension for a vector space or subspace - Find the coordinates of a vector with respect to a given basis and change the basis using transition matrices - Define and classify linear maps between vector spaces and find their domains, codomains, ranges, and null spaces - Find the kernel and image of a linear map and use them to determine whether a linear map is one-to-one or onto - Represent a linear map using a matrix and perform matrix operations such as addition, multiplication, and inversion - Use different methods and tools to solve systems of linear equations, such as Gaussian elimination, row reduction, and inverse matrices This course is suitable for anyone who wants to learn or review the basics of vector spaces and linear maps and their applications. It is especially useful for students and professionals in algebra, geometry, analysis, differential equations, optimization, cryptography, computer graphics, data science, and other related fields. By the end of this course, you will have a solid foundation of the theory and practice of vector spaces and linear maps and their operations. You will also be able to apply the knowledge and skills you learned to real-world problems and challenges that involve vector spaces and linear maps. Once enrolled, you have access to dynamic video lessons, interactive quizzes, and live chat support for an immersive learning experience. You engage with clear video explanations, test your understanding with instant-feedback quizzes and interact with our expert instructor and peers in the chat room. Join a supportive learning community to exchange ideas, ask questions, and collaborate with peers as you master the material, by enrolling right away.