数值线性代数是一门研究在计算机上进行线性代数计算，特别是矩阵运算的算法的学科，是工程学和计算科学问题中的基本部分，这些问题包括图像处理、信号处理、金融工程学、材料科学模拟、结构生物学、数据挖掘、生物信息学、流体动力学和其他很多领域。这类软件多依赖于解决多种数值线性代数问题的先进算法的发展、分析和实现，在很大程度上是依靠矩阵在有限差分法和有限元法中的作用。

数值线性代数中的常见问题包括下列计算问题：LU分解、QR分解、奇异值分解、特征值。

Numerical linear algebra is the study of algorithms for performing linear algebra computations, most notably matrix operations, on computers. It is often a fundamental part of engineering and computational science problems, such as image and signal processing, telecommunication, computational finance, materials science simulations, structural biology, data mining, bioinformatics, fluid dynamics, and many other areas. Such software relies heavily on the development, analysis, and implementation of state-of-the-art algorithms for solving various numerical linear algebra problems, in large part because of the role of matrices in finite difference and finite element methods.