- #1
EnglsihLearner
- 11
- 1
What is the difference between orthogonal transformation and linear transformation?
EnglsihLearner said:What is the difference between orthogonal transformation and linear transformation?
Orthogonal transformation is a type of linear transformation that preserves angles and distances between vectors, while linear transformation refers to a change in the position or orientation of a vector.
A transformation is orthogonal if the dot product of two vectors is equal to the dot product of their transformed vectors. A transformation is linear if it follows the properties of linearity, such as preserving scalar multiplication and addition.
Yes, a transformation can be both orthogonal and linear. This means that it preserves both angles and distances, while also following the properties of linearity.
Some examples of orthogonal transformations include rotations, reflections, and the identity transformation.
Orthogonal transformations are commonly used in computer graphics to rotate or reflect images. Linear transformations are used in various fields, such as engineering and physics, to model changes in variables or systems.