Linear algebra has a wide range of applications. The applications of linear algebra increase over time as computing power increases. Some applications of linear algebra include:
Applications to engineering, physics, biology, economics, and statistics.
Computer science, including computer graphics.
Applications to data science and machine learning.
Oil exploration, ships searching for offshore oil deposits solve thousands of systems of linear equations every day. The seismic data for the equations are obtained from underwater shock waves created by explosions from air guns.
Linear programming, airlines scheduling flight crews, monitoring the location of aircraft.
Network flow (e.g. the internet, electrical networks, traffic flow, etc.), relies on linear algebra and linear systems of equations. Google's PageRank, ranking websites.
Chemistry, the geometry of molecules such as methane, balancing chemical equations as a system of equations.
Psychology, factor analysis.
pg. 1 Leontief economic analysis, ch.1.6 and 2.6, applications of linear algebra (in particular, systems of linear equations).
Robotics.
Applications to cryptography, using matrices.
Linear algebra also provides the foundations for other advanced topics in mathematics, including:
