pöördtransformatsioon

Pöördtransformatsioon, often translated as inverse transformation or inversion, is a mathematical concept used to describe operations that can be "undone" by applying another operation. In essence, if applying an operation A to a value x results in a value y, then the inverse transformation of A, let's call it A⁻¹, will take y back to x, such that A⁻¹(y) = x. This fundamental idea appears in various branches of mathematics and computer science.

In linear algebra, a matrix has an inverse if and only if its determinant is non-zero. Multiplying a vector by a matrix and then by its inverse results in the original vector. This property is crucial for solving systems of linear equations. In calculus, integration is the inverse operation of differentiation. The integral of a function's derivative returns the original function, up to an additive constant.

The concept of inversion is also prevalent in geometry. Geometric inversions transform lines and circles into other lines and circles, with specific rules governing the transformation of points. In computer graphics and image processing, inverse transformations are used to map pixels from a transformed coordinate system back to their original positions, enabling operations like undoing rotations or scaling. The definition and application of a pöördtransformatsioon depend heavily on the specific context and the nature of the initial transformation.