The concepts of linear algebra are essential for understanding the theory behind ML because they help us understand how ML algorithms work under the hood. Also, most ML algorithm definitions use linear algebra terms.

Linear algebra is not only a handy mathematical instrument, but also the concepts of linear algebra can be very efficiently implemented with modern computer architectures. The rise of ML, and especially deep learning, began after significant performance improvement of the modern Graphics Processing Unit (GPU). GPUs were initially designed to work with linear algebra concepts and massive parallel computations used in computer games. After that, special libraries were created to work with general linear algebra concepts. Examples of libraries that implement basic linear algebra routines are Cuda and OpenCL, and one example of a specialized linear algebra library is cuBLAS. Moreover, it became more common to use general-purpose graphics processing units (GPGPUs) because these turn the computational power of a modern GPU into a powerful general-purpose computing resource.

Also, Central Processing Units (CPUs) have instruction sets specially designed for simultaneous numerical computations. Such computations are called vectorized, and common vectorized instruction sets are AVx, SSE, and MMx. There is also a term Single Instruction Multiple Data (SIMD) for these instruction sets. Many numeric linear algebra libraries, such as Eigen, xtensor, VienaCL, and others, use them to improve computational performance.