Numerical Linear Algebra
Numerical Linear Algebra is a branch of applied mathematics and computer science that focuses on developing and implementing algorithms for performing linear algebra computations efficiently and accurately on computers. It deals with solving problems involving matrices and vectors, such as linear systems, eigenvalue problems, and matrix factorizations, using numerical methods rather than exact symbolic approaches. This field is essential for handling large-scale computations in scientific and engineering applications where exact solutions are impractical.
Developers should learn Numerical Linear Algebra when working on applications that involve large datasets, simulations, machine learning, or scientific computing, as it provides the foundational algorithms for tasks like solving linear equations, dimensionality reduction, and optimization. It is crucial in fields like data science, computer graphics, and engineering, where efficient matrix operations are needed to process real-world data with numerical stability and performance. For example, it underpins techniques in deep learning (e.g., backpropagation), physics simulations, and financial modeling.