Definition

1. Adjective:

   • Unchanging in nature or value: Describes something that remains constant and does not vary under specified conditions.
   • Unaffected by a designated operation or transformation: In mathematics and science, describes a quantity, property, or function that remains the same when a particular operation is performed.

2. Noun:

   • A quantity or property that remains unchanged: In mathematics and physics, a specific feature (like a number, property, or function) that does not change when a particular transformation is applied to the system it describes.

Examples of Usage

• Adjective:
  • The speed of light in a vacuum is an invariant constant.
  • Her daily routine was remarkably invariant, following the same schedule for years.
• Noun:
  • In physics, the spacetime interval is a fundamental invariant.
  • The mathematician studied the invariants of the geometric transformation.

Advanced Usage

• "Lorentz invariant": In physics, a quantity that remains unchanged under a Lorentz transformation, which is fundamental to the theory of relativity.
  • The laws of physics must be Lorentz invariant.
• "Topological invariant": In mathematics, a property of a topological space that remains unchanged under homeomorphisms (continuous deformations).
  • Euler characteristic is a well-known topological invariant.

Variants and Related Words

• Invariance (n): The state or quality of being invariant; constancy.
  • The invariance of the physical law was proven experimentally.
• Invariably (adv): In every case; always.
  • She is invariably punctual.

Synonyms

• Constant: Remaining the same over a period of time.
• Unchanging: Not changing; remaining the same.
• Fixed: Not subject to change or variation.

Antonyms

• Variable: Liable to change; not constant.
• Changing: Undergoing change or alteration.

Adjective

1. unvarying in nature
   • maintained a constant temperature
   • principles of unvarying validity
2. unaffected by a designated operation or transformation

Noun

1. a feature (quantity or property or function) that remains unchanged when a particular transformation is applied to it