Inverse
An inverse is a value or operation that reverses the effect of another value or operation under a specified composition rule.
Geometry for Programmers
An inverse transformation is a mapping that reverses another transformation by recovering each original point from its transformed point.
- How it is used
- Reverses composed projective transformations to recover original geometric points efficiently.
- How deep it goes
- Works through matrix-based recovery of rectangle corners and notes faster projective alternatives, without deriving a general inverse algorithm.
- Examples
- Uses a rectangle rotated about its center and restored with a SymPy inverse matrix.
- What you can do after
- Apply it via SymPy matrix inversion to restore points after a composed projective transformation.
Elliptic Curve Cryptography for Developers
An inverse is a polynomial that multiplies with another polynomial to produce the multiplicative identity modulo a specified irreducible polynomial.
- How it is used
- Supports division and elliptic-curve calculations over extension fields.
- How deep it goes
- Derives the extended-Euclidean invariant and translates initialization, normalization, updates, termination, and cleanup into C.
- Examples
- Uses clock-style modular arithmetic and the irreducible polynomial x² + x + 3 modulo 43 as concrete finite-field examples.
- What you can do after
- Build it from scratch as a polynomial-inversion routine and reuse it to implement division modulo a prime polynomial.
Read how Elliptic Curve Cryptography for Developers explains inverse →
Related concepts
- x gateequivalent to · The X gate is a single-qubit quantum gate that exchanges the computational-basis states zero and one.
- biquadratic transformationuses · A biquadratic transformation is a mapping described by expressions that are quadratic in each of two input variables.
- projective transformationused by · A projective transformation is a mapping of projective-space points represented by homogeneous linear coordinates that preserves incidence but may not preserve parallelism.
- adjointequivalent to · The adjoint of a complex matrix or linear operator is its conjugate transpose.
- polynomial divisionused by · Polynomial division expresses a dividend as a divisor multiplied by a quotient plus a remainder of lower degree than the divisor.
- polynomial normalizationused by · Polynomial normalization scales every coefficient by the inverse of the leading coefficient to make a polynomial monic.
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