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# Homothetic-transformation

noun, Mathematics.
1.
(def 1).
noun, Mathematics.
1.
Also called homothetic transformation. a mapping of a set by which each element in the set is mapped into a positive constant multiple of itself, the same constant being used for all elements.
2.
an operation performed upon a square matrix that leaves invariant its characteristic polynomial, trace, and determinant. The transformation is obtained by multiplying the given matrix on one side by any nonsingular matrix and on the other by the inverse of that nonsingular matrix.

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• Homothety

[hoh-muh-thet-ik, hom-uh-] /ˌhoʊ məˈθɛt ɪk, ˌhɒm ə-/ adjective, Geometry. 1. similar; similarly placed.

• Homotonic

homotonic ho·mo·ton·ic (hō’mə-tŏn’ĭk) adj. Having uniform tension, as of muscular contraction.

• Homotopic

homotopic ho·mo·top·ic (hō’mə-tŏp’ĭk) adj. Relating to or occurring in the same or corresponding place or part of the body.

• Homotopy

[huh-mot-uh-pee, hoh-] /həˈmɒt ə pi, hoʊ-/ noun, plural homotopies. Mathematics. 1. the relation that exists between two mappings in a topological space if one mapping can be deformed in a continuous way to make it coincide with the other.

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