invarianta

Invarianta, in Romanian, refers to the mathematical and scientific concept of invariance or an invariant property. An invariant is a property that remains unchanged under a defined set of transformations or operations. This idea appears across several disciplines and is central to identifying structure within systems.

In mathematics, invariants are used to distinguish objects under transformations. For example, in Euclidean geometry, the distance between two points is invariant under rigid motions such as translations and rotations. In linear algebra, certain quantities are invariant under similarity transformations; the trace and determinant of a matrix are preserved when the matrix is conjugated by an invertible change of basis, and eigenvalues are invariants of similarity classes.

In physics, invariants provide constants of motion or frame-independent quantities. The spacetime interval is invariant under Lorentz transformations in special relativity, and conserved quantities arise from symmetries via Noether's theorem.

In computer science and logic, invariants are conditions that remain true throughout program execution. Loop invariants are asserted to hold before and after each iteration, enabling formal verification and reasoning about correctness.

See also: invariance, invariant, symmetry, Noether's theorem, conservation law.