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Linear algebra is the branch of mathematics concerned with the study of vectors, vector spaces (also called linear spaces), and linear transformations between these spaces, such as rotating a shape, scaling it up or down, translating it (i.e., moving it), etc. These concepts are fundamental to understanding various mathematical models in science and engineering, including those related to geometry, physics, computer graphics, machine learning, and many others. In the hierarchy of Science/Mathematics/Abstract Algebra, linear algebra can be thought of as a way to apply abstract algebraic structures (like groups and fields) to real-world problems, particularly in the context of vectors and transformations. It provides a powerful framework for modeling and solving complex problems involving quantities that change linearly with respect to one another, making it an essential tool for scientists, engineers, and mathematicians alike.