kääntävyys

Kääntävyys refers to the concept of invertibility in mathematics, particularly in the context of functions and matrices. A function is considered kääntävä if it has an inverse function. This means that for every output value in the range of the function, there is a unique input value in its domain that maps to it. In other words, if a function f maps x to y, then its inverse function, denoted f⁻¹, maps y back to x. This property is crucial for solving equations and understanding transformations.

Similarly, a square matrix is kääntävä if it has a multiplicative inverse. An inverse matrix, when multiplied by the original matrix, results in the identity matrix. This implies that the determinant of the matrix is non-zero. Kääntävä matrices are essential in linear algebra for solving systems of linear equations, performing transformations in geometric spaces, and in various applications within physics, engineering, and computer science. The existence of an inverse allows for the "undoing" of the operation represented by the matrix or function. If a function or matrix is not kääntävä, it is referred to as singular or non-invertible.