similarity transformation: meaning, definition, pronunciation and examples
LowFormal, Technical
Quick answer
What does “similarity transformation” mean?
A geometric transformation that changes the size and position of a figure while preserving its shape, angles, and proportions.
Audio
Pronunciation
Definition
Meaning and Definition
A geometric transformation that changes the size and position of a figure while preserving its shape, angles, and proportions.
In mathematics, a mapping of the plane (or space) onto itself that multiplies all distances by the same positive scale factor, often involving translation, rotation, and uniform scaling. In linear algebra, a transformation between matrices of the form B = P⁻¹AP, where P is invertible, preserving eigenvalues and matrix properties.
Dialectal Variation
British vs American Usage
Differences
No significant lexical differences. Minor potential spelling variations (e.g., 'centre' vs. 'center') in surrounding text.
Connotations
None beyond technical mathematical meaning.
Frequency
Equally low and restricted to academic/technical fields in both varieties.
Grammar
How to Use “similarity transformation” in a Sentence
The similarity transformation (of A) maps point X to point Y.Two figures are related by a similarity transformation.We apply a similarity transformation to the matrix.Vocabulary
Collocations
Examples
Examples of “similarity transformation” in a Sentence
adjective
British English
- The two triangles are similarity-related.
- They studied similarity properties of geometric figures.
American English
- The two triangles are similarity-related.
- They studied similarity properties of geometric figures.
Usage
Meaning in Context
Business
Virtually never used, except possibly in highly technical sectors like CAD software development.
Academic
Core term in geometry, linear algebra, and computer graphics courses and textbooks.
Everyday
Extremely rare; would be confusing to non-specialists.
Technical
Standard term in mathematics, engineering (especially signal processing, where it refers to a specific matrix operation), and computer vision.
Vocabulary
Synonyms of “similarity transformation”
Strong
Neutral
Weak
Vocabulary
Antonyms of “similarity transformation”
Watch out
Common Mistakes When Using “similarity transformation”
- Confusing it with 'congruent transformation' (which also preserves size).
- Using it to describe transformations that change shape (e.g., stretching unevenly).
- Omitting 'transformation' and just saying 'similarity', which is ambiguous.
FAQ
Frequently Asked Questions
Yes, a rotation is a special case of a similarity transformation where the scale factor is 1 (it preserves size as well as shape).
'Congruent' figures are identical in shape AND size, related by an isometry (translation, rotation, reflection). 'Similar' figures are identical in shape but not necessarily size, related by a similarity transformation (which includes isometries and scaling).
No, by definition, a similarity transformation preserves all angles exactly. If angles change, it is not a similarity transformation.
They are fundamental in computer graphics for scaling objects, in computer vision for object recognition (matching templates at different scales), and in cartography for creating map scales.
A geometric transformation that changes the size and position of a figure while preserving its shape, angles, and proportions.
Similarity transformation is usually formal, technical in register.
Similarity transformation: in British English it is pronounced /ˌsɪm.ɪˈlær.ɪ.ti ˌtræns.fəˈmeɪ.ʃən/, and in American English it is pronounced /ˌsɪm.əˈlær.ə.t̬i ˌtræns.fɚˈmeɪ.ʃən/. Tap the audio buttons above to hear it.
Learning
Memory Aids
Mnemonic
Think of a photocopier that enlarges or reduces a document. The copy is 'similar' to the original – same content, same layout, just a different size. That's a real-world similarity transformation.
Conceptual Metaphor
MATHEMATICAL RELATIONSHIPS ARE SPATIAL TRANSFORMATIONS.
Practice
Quiz
Which of the following is NOT necessarily preserved under a similarity transformation?