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Glite Dictionary
💻 Accepts supertypes 🔄 Reverses mappings ↔️ Changes oppositely
contravariant

contravariant

9.9
Changes the direction of mappings between mathematical structures
  • adjective
  • /ˌkɒntrəˈveɪərənt/
  • Specialized
: contravariante
  • The behavior of the contravariant vector is different when the coordinate system is altered compared to covariant vectors.

Examples

  • That's the covariant derivative of the contravariant components of a tensor.

  • So this is sort of the archetype of A of a contravariant vector component.

  • In mathematics, a contravariant function transforms its inputs in the opposite direction to the changes in the output structure.

  • When studying tensors, understanding the properties of contravariant components is essential for applying transformations correctly.

Surface Forms

contravariant positive

Morphology

contravariant = variant (semi-transparent) = contra + variant

The prefix 'contra-' suggests opposition, but the specific mathematical meaning requires specialized knowledge.

Etymology

Contravariant comes from contra- 'against' and variant (like English vary) 'change', so it literally means 'changing against' the usual direction. That's why a contravariant functor or map in mathematics reverses the direction of mappings between structures.