An orthogonal transformation is a mathematical operation that preserves the length of vectors and the angles between them. This means that when a vector is transformed using an orthogonal transformation, its magnitude remains unchanged, and the geometric relationships between vectors are maintained. Common examples include rotations and reflections in Euclidean space. In linear algebra, orthogonal transformations can be represented by orthogonal matrices, which have the property that their transpose is equal to their inverse. This property ensures that the transformation does not distort the original shape or size of objects in vector spaces, making orthogonal transformations useful in various applications, including computer graphics and data analysis.