Linear algebra - Wikipedia

Linear algebra is a fundamental branch of mathematics that studies linear equations, vector spaces, and linear transformations. Key concepts in linear algebra include vector spaces, linear transformations, matrices, determinants, eigenvalues, and eigenvectors. Linear algebra has numerous applications across various scientific fields such as physics, engineering, computer science, economics, and quantum mechanics.Some of the key applications of linear algebra are:1. Computer graphics: Linear algebra is used extensively in computer graphics to perform transformations on 3D models, such as rotations, translations, and projections.2. Robotics: Linear algebra is used in robotics to solve the kinematics and dynamics of robots, which involve solving systems of linear equations to determine the position and velocity of the robot's joints and the forces acting on it.3. Signal processing: Linear algebra is used in signal processing to perform filtering, convolution, and other operations on signals.4. Data analysis: Linear algebra is used in data analysis to solve systems of linear equations that arise from statistical problems, such as regression analysis and principal component analysis.5. Quantum mechanics: Linear algebra is used in quantum mechanics to represent the wave function of a quantum system and to solve the Schrödinger equation, which is a partial differential equation that describes the evolution of the wave function over time.For those interested in learning more about linear algebra, there are various resources available, including Khan Academy's Linear Algebra Course, MIT OpenCourseWare's Linear Algebra course, Wolfram MathWorld, GeoGebra, and Gilbert Strang's Linear Algebra and Its Applications book.