Jacobian conjecture
conjecture asserting that, over a characteristic-zero field K, given a polynomial map f: Kⁿ → Kⁿ, if its Jacobian determinant J: Kⁿ → K is a nonzero constant map, then f admits a polynomial inverse g: Kⁿ → Kⁿ
Press Enter · cited answer in seconds
0 sources
Jacobian conjecture
Summary
Jacobian conjecture is a conjecture[1]. It draws 93 Wikipedia views per month (conjecture category, ranking #14 of 128).[2]
Key Facts
- Jacobian conjecture is credited with the discovery of Ott-Heinrich Keller[3].
- Jacobian conjecture's instance of is recorded as conjecture[4].
- Jacobian conjecture's instance of is recorded as Smale's problems[5].
- Carl Gustav Jacob Jacobi is named after Jacobian conjecture[6].
- Jacobian conjecture's Freebase ID is recorded as /m/04g6f9[7].
- Jacobian conjecture's defining formula is recorded as \left[\hat{b}^\dagger, \hat{b}^\dagger \right]_- = 0[8].
- Jacobian conjecture's nLab ID is recorded as Jacobian conjecture[9].
- Jacobian conjecture's maintained by WikiProject is recorded as WikiProject Mathematics[10].
- Jacobian conjecture's Microsoft Academic ID is recorded as 92014495[11].
Body
Designation and Status
Recorded instance of include conjecture[4] and Smale's problems[5].
History and Context
Carl Gustav Jacob Jacobi is named after Jacobian conjecture[6].
Why It Matters
Jacobian conjecture draws 93 Wikipedia views per month (conjecture category, ranking #14 of 128).[2] It has Wikipedia articles in 10 language editions, a strong signal of global cultural recognition.[12]