Dick said:Tr(ABC)=Tr(CAB).
An orthogonal transformation, also known as an orthogonal matrix, is a type of linear transformation in which the length and angle of vectors are preserved. This means that the transformation does not change the shape or size of the objects being transformed.
An orthogonal transformation is different from other types of transformations, such as rotations and reflections, because it preserves both length and angle. This means that the transformed object will be an exact copy of the original, just in a different position or orientation.
Orthogonal transformations are commonly used in computer graphics, particularly in 3D graphics, to rotate and scale objects without distorting the image. They are also used in signal processing, such as in Fourier transformations, to analyze and modify signals.
To perform an orthogonal transformation, you need to multiply the original vector or matrix by an orthogonal matrix. This can be done using various mathematical operations, such as matrix multiplication or rotation formulas.
Yes, an orthogonal transformation can be undone by multiplying the transformed vector or matrix by the inverse of the original orthogonal matrix. This will result in the original vector or matrix being restored to its original form.