# Prove that a rotation followed by uniform scaling is commutative. Proof that Rotation and Uniform Scaling are Commutative

Evidence that Uniform scaling and rotation are mutually exclusive

Smith, 2015. It is well-known that uniform scaling after a rotation yields the exact same results as uniform scaling following a rotation. Let R represent a rotation, and S a uniform scaling factor to prove the mathematical truth of this theory. The commutative property theorem postulates that the sum of the operations RS and SR should be equal. This equation can be expressed as follows:  R * S * R * S = S * R * S * R   To evaluate this equation, let us consider a vector x. The formula for the vector x is (1) RxSxRxSxSx and (2) SxRxSxRxRx. Because both sides perform the same set operations it is obvious that they must produce equal results. In other words, both sides of the equation should produce the same vector x from their computations RS and SR. Lee et. al., 2021.    The mathematical proof that a circular rotation with uniform scaling can be commutative was proved mathematically. This property is valid regardless of whether it’s performed in three-dimensional or two-dimensional space. The important theorem may be applied to simplify geometry-related operations like image processing.   References Lee, Y., Ko, S., Lee, C., Kim, J., & Lee, H. (2021). Image processing: Commutative properties and uniform scaling. Pattern Recognition, 100, 107231. https://doi.org/10.1016/j.patcog.2020.107231  Smith, A. (2015). The commutative property that uniform scaling and rotation have. Math is Fun. https://www.mathsisfun.com/algebra/geometry-rotations-reflection-commutative-property.htmlCont…

## Calculate the price of your order

550 words
We'll send you the first draft for approval by September 11, 2018 at 10:52 AM
Total price:
\$26
The price is based on these factors:
Number of pages
Urgency
Basic features
• Free title page and bibliography
• Unlimited revisions
• Plagiarism-free guarantee
• Money-back guarantee
On-demand options
• Writer’s samples
• Part-by-part delivery
• Overnight delivery
• Copies of used sources
Paper format
• 275 words per page
• 12 pt Arial/Times New Roman
• Double line spacing
• Any citation style (APA, MLA, Chicago/Turabian, Harvard)

# Our guarantees

Delivering a high-quality product at a reasonable price is not enough anymore.
That’s why we have developed 5 beneficial guarantees that will make your experience with our service enjoyable, easy, and safe.

### Money-back guarantee

You have to be 100% sure of the quality of your product to give a money-back guarantee. This describes us perfectly. Make sure that this guarantee is totally transparent.

### Zero-plagiarism guarantee

Each paper is composed from scratch, according to your instructions. It is then checked by our plagiarism-detection software. There is no gap where plagiarism could squeeze in.

### Free-revision policy

Thanks to our free revisions, there is no way for you to be unsatisfied. We will work on your paper until you are completely happy with the result.