similarity
Pluralsimilarities
- 1The quality of looking very much like something else.
The similarity between the forged painting and the original fooled several experts.
Witnesses commented on the striking similarity in the two brothers' appearance.
Similarresemblance, likeness, closeness
Oppositedifference, contrast
Note
Everyday resemblance works both as a mass noun and as a countable one. Uncountable, it names likeness in general, as when the similarity of a forgery fools experts. Countable, a similarity is one particular point of likeness, so you can list the similarities between two faces. The word came into English from French similarité and is built as English would build it, from similar plus -ity.
- 2The relation that holds between things which share one or more properties.
Philosophers disagree about whether similarity reduces to shared properties or counts as a basic relation.
Biological classification often rests on the similarity among organisms' genetic traits.
Similarresemblance, likeness
Oppositedifference
Note
Philosophy reduces likeness to logic: two things are similar when they share at least one property. Theorists disagree about how that sharing works, explaining it either through common universals or through a basic relation of resemblance. William Hamilton's Lectures (1859–1860) warn of the pull it has on reasoning: hardly is a similarity detected between two or three facts than men hasten to extend it to all.
- 3In geometry, a mapping of Euclidean space under which angles stay the same and every distance is scaled by one common factor.
Every similarity maps a figure onto another with the same shape but a different size.
Composing two similarities always produces another similarity.
Note
Geometry turns the word into the name of a map. A similarity stretches or shrinks every distance by one fixed positive factor and leaves angles untouched, so each figure lands on a geometrically similar copy. Because it names a transformation, it counts freely: a similarity, two similarities. That sets it apart from the matrix relation, where the noun names a property rather than a map.
- 4The property holding between two matrices when one can be obtained from the other through a change of basis.
The similarity of two matrices guarantees they share the same eigenvalues.
To prove similarity, you find an invertible matrix that turns one into the other.
Note
In linear algebra the word names a relation between square matrices. A and B are similar when B = P⁻¹AP for some invertible matrix P, which means they describe the same linear map in a different basis. Similar matrices therefore share eigenvalues, trace, determinant and characteristic polynomial, so similarity is the usual test of whether two matrices are essentially the same.
Practice
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Origin
From French "similarité," and formed morphologically from "similar" plus the suffix "-ity."