käänteiskartta

Käänteiskartta, also known as an inverse map or reverse map, is a concept in mathematics and computer science that refers to the process of finding the preimage of a given set or element under a function. In other words, it involves determining the set of all inputs that map to a specific output under a given function. This concept is particularly useful in various fields such as cryptography, data analysis, and optimization problems.

In a more formal context, given a function f: X → Y, the inverse map of a subset B of Y is defined as the set of all elements in X that map to elements in B under the function f. Mathematically, this can be expressed as f^-1(B) = {x ∈ X | f(x) ∈ B}. The inverse map is not always a function itself, as it may not be well-defined for all elements in the codomain Y. This is because multiple elements in X can map to the same element in Y, leading to ambiguity in the inverse mapping.

The concept of an inverse map is closely related to the idea of an inverse function, which is a function that "undoes" the action of another function. However, not all functions have an inverse function, and even when they do, the inverse map may not be a function in the traditional sense. The study of inverse maps and their properties is a fundamental topic in various branches of mathematics and has applications in diverse fields.