Vector Operations
TLDR: Vector operations are mathematical and computational tasks performed on vectors, which are arrays or sequences of numbers representing quantities with both magnitude and direction. In computing, these operations are optimized for handling large datasets and include tasks like addition, subtraction, dot product, and cross product. Vector operations are fundamental to fields like physics, machine learning, and computer graphics, enabling efficient computations on multi-dimensional data.
https://en.wikipedia.org/wiki/Vector_(mathematics_and_computing)
Vector operations leverage Single Instruction Multiple Data (SIMD) architecture to perform computations on multiple data points simultaneously, significantly boosting performance. For example, adding two vectors involves element-wise addition, which can be executed in parallel using modern CPUs or GPUs. Libraries and frameworks like NumPy in Python and Eigen in C++ provide optimized implementations of vector operations, making them accessible to developers across diverse domains.
https://numpy.org/doc/stable/reference/routines.linalg.html
Applications of vector operations are extensive, ranging from solving linear algebra problems to rendering realistic 3D graphics in games. In machine learning, vector operations are used for tasks like calculating weights and biases in neural networks. Advanced tools such as TensorFlow and PyTorch build upon these operations to enable efficient computation on high-dimensional data. Mastering vector operations is essential for developers working in computational science, data analysis, and algorithm optimization.