invariance

Thân thiện

The invariance of the shape is maintained under rotation.

Definition

Noun: 1. The property of remaining unchanged under a specific transformation or set of operations. This is a fundamental concept in mathematics and physics, where a system, equation, or quantity is said to have invariance if it does not change when a particular operation (like rotation, translation, or time shift) is applied. 2. The quality of being unvarying, constant, or resistant to change. This describes a state of stability or consistency over time or under different conditions.

Examples of Usage

• Scientific/Mathematical Context:
  • The invariance of the speed of light is a cornerstone of Einstein's theory of relativity.
  • The equation demonstrates invariance under rotation, meaning its form is the same in any rotated coordinate system.
• General Context:
  • The invariance of his daily routine was both comforting and monotonous.
  • The experiment tested the invariance of the material's properties across different temperature ranges.

Advanced Usage

• Symmetry and Invariance: In theoretical physics, a symmetry of a physical system corresponds directly to an invariance under a transformation, leading to a conservation law (e.g., invariance under time translation leads to conservation of energy).
• Scale Invariance: A property where an object or law does not change if scales of length, energy, or other variables are multiplied by a common factor. Fractals often exhibit scale invariance.

Variants and Related Words

• Invariant (Adjective/Noun):
  • (Adj.) Unchanging, constant. The fundamental laws are invariant across the universe.
  • (N.) A quantity, property, or function that remains unchanged. The speed of light is an invariant.
• Covariance (Noun): A related concept where quantities change in a specific, coordinated way under transformation, as opposed to remaining strictly invariant.

Synonyms

• Constancy
• Stability
• Immutability
• Unchangeability
• Fixedness

Antonyms

• Variance
• Changeability
• Variation
• Fluctuation
• Instability

Học thuật

Noun

1. the nature of a quantity or property or function that remains unchanged when a given transformation is applied to it
   • the invariance of the configuration under translation
2. the quality of being resistant to variation

Từ đồng nghĩa

• invariability
• invariableness