Vectors, Matrices, and Multidimensional Arrays

Vectors, matrices, and arrays of higher dimensions are essential tools in numerical computing. They enable us to represent and manipulate data efficiently, particularly when computations need to be repeated for a set of input values. By formulating computations in terms of array operations, we can perform vectorized computing, eliminating the need for many explicit loops over array elements by applying batch operations to the array data. Vectorized computing results in concise and more maintainable code, allowing the implementation of array operations to be delegated to more efficient low-level libraries. As a result, vectorized computations can be significantly faster than sequential element-by-element computations. This is particularly important in interpreted languages like Python, where looping over arrays element-by-element incurs significant performance overhead.