What does "automorphism" mean?
An isomorphism of a mathematical object or system of objects onto itself.
Automorphism
noun
noun ·Rare ·Advanced level
Meaning at a glance
- Primary sense: An isomorphism of a mathematical object or system of objects onto itself.
- Grammar: automorphism is listed as noun.
- Usage evidence: Since every linear automorphism of V fixes 0 our interest in the transitivity properties of GL(V) is confined to its action on V* = V - {0}. GL(V) is transitive on V* since any two elements of V* may be chosen as the initial members of two ordered bases; it is not in general 2-transitive because there is no linear automorphism taking an independent pair to a dependent pair.
How to use "automorphism"
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Meaning check
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Source and review context
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Before you rely on this definition
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Compare nearby meanings
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Definition decision workflow
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Definitions
Noun
- 1 An isomorphism of a mathematical object or system of objects onto itself. countable, uncountable
"Since every linear automorphism of V fixes 0 our interest in the transitivity properties of GL(V) is confined to its action on V* = V - {0}. GL(V) is transitive on V* since any two elements of V* may be chosen as the initial members of two ordered bases; it is not in general 2-transitive because there is no linear automorphism taking an independent pair to a dependent pair."
- 2 The ascription to others of one's own characteristics or of one's own perceived characteristics. countable, uncountable
"1895 Hiram M. Stanley: Studies in the Evolutionary Psychology of Feeling. MacMillan Sensation for us is a complex of sensations plus perceptions and other cognitive and emotional elements which lie beyond early mind, but which by an inevitable automorphism we interpret into early forms. This automorphism with the child is complete, and is never perfectly effaced even in the most accomplished psychologist. . . . But when we come to interpret the psychoses of the lower animals in connection with sexuality we may still more easily slip into a doubtful automorphism. Thus to say with Darwin, "When we behold a male bird elaborately displaying ... before the female, ... it is impossible to doubt that she admires the beauty of her male partner" (Descent of Man), or more strongly still with Grant Allen, "Every crow must think its own mate beautiful" (Mind, v. 448), we too easily take for granted that these birds would feel like ourselves in corresponding circumstances."
Example
"Since every linear automorphism of V fixes 0 our interest in the transitivity properties of GL(V) is confined to its action on V* = V - {0}. GL(V) is transitive on V* since any two elements of V* may be chosen as the initial members of two ordered bases; it is not in general 2-transitive because there is no linear automorphism taking an independent pair to a dependent pair."
Common questions
How do you use "automorphism" in a sentence?
Since every linear automorphism of V fixes 0 our interest in the transitivity properties of GL(V) is confined to its action on V* = V - {0}. GL(V) is transitive on V* since any two elements of V* may be chosen as the initial members of two ordered bases; it is not in general 2-transitive because there is no linear automorphism taking an independent pair to a dependent pair.
Etymology
From auto- + morphism.