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Definition of Identity element
1. Noun. An operator that leaves unchanged the element on which it operates. "The identity under numerical multiplication is 1"
Definition of Identity element
1. Noun. (algebra) A member of a structure which, when applied to any other element via a binary operation induces an identity mapping; more specifically, given an operation ''*'', an element ''I'' is ¹
¹ Source: wiktionary.com
Lexicographical Neighbors of Identity Element
Literary usage of Identity element
Below you will find example usage of this term as found in modern and/or classical literature:
1. Projective Geometry by Oswald Veblen, John Wesley Young (1910)
"An element i of G is called an identity element, and an element ... There is only
one identity element in G. For every element a of G there is only one ..."
2. Geometric Computing Science: First Steps by Robert Hermann (1991)
"The identity element is the identity matrix. With these definitions, the ‘monoid'
conditions 9.2-9.3 follow from properties of matrix multiplication. ..."
3. Cartanian Geometry, Nonlinear Waves, and Control Theory by Robert Hermann (1979)
"The identities obtained in this way show that A . . , A . , . . . agree at the
iJ jk identity element with linear combinations of the partial derivative ..."
4. Invariant Measures on Groups and Their Use in Statistics by Robert A. Wijsman (1990)
"F, by requiring the following properties of V: (i) V is an associative algebra
over F with an identity element; (ii) V contains Vl] (iii) u Au = 0 for every ..."
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