Linear Algebra: Linear Transformations & Vector Spaces
Exploring the foundations of linear algebra through the study of linear transformations and vector spaces"
What you will learn
Learn what linear transformations are and how to define them.
Learn what a basis is and how to change basis.
Learn about span, row space, column space, null space and how these concepts relate to linear transformations.
Learn what eigenvalues & eigenvectors are and how to derive them.
Learn what an abstract vector space is.
Why take this course?
In this course, you will learn about some important concepts in math called linear transformations and vector spaces. These concepts are used to understand how to work with shapes and patterns in math.
We will learn about matrices, which are like grids of numbers that can be used to represent linear transformations. We will also learn about vectors, which are like arrows that can be added and subtracted to find new positions.
One of the main things we will learn about is called a basis, which is a set of vectors that can be used to represent any other vector in a vector space. We will also learn about something called the Gram-Schmidt process, which is a way to turn a set of vectors into an "orthonormal" basis, which means that the vectors are all perpendicular to each other and have a length of 1.
Throughout the course, we will practice using these concepts and techniques to solve problems, such as finding Transformation matrices, transforming vectors, and solving systems of linear equations.
This course is a good opportunity to learn more about math and how it can be used to understand patterns and shapes in the world around us. This course is for you if you are looking to pursue a career in a mathematical field such as Data Science, you're a student, or you are just looking to further your mathematics education.
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