👉 Index math, also known as index arithmetic or index notation, is a mathematical system used to perform arithmetic operations on complex numbers and other mathematical objects with multiple indices. It extends the standard real number arithmetic by incorporating additional indices, typically representing dimensions or degrees of freedom, to describe the structure of these objects. For instance, in three-dimensional space, a vector can be represented with one index (position), and its magnitude and direction are captured by two indices (magnitude and unit vector). Index math allows for concise and efficient manipulation of these objects, enabling operations such as addition, subtraction, multiplication, and division to be performed in a way that respects their multi-dimensional nature. This system is particularly useful in fields like physics, engineering, and computer graphics, where objects often have multiple dimensions and require precise mathematical descriptions.
