Examples
Examples
Try the starting example
- State matrix A
- [[-1,1],[0,-2]]
- Convention: 0 continuous, 1 discrete
- 0
- Numerical boundary tolerance
- 1e-06
- Eigenvalue coordinates (JSON)
- [[-2,0],[-1,0]]
- Linear stability classification
- asymptotically stable
Try another scenario
- State matrix A
- [[0,1],[0,-2]]
- Convention: 0 continuous, 1 discrete
- 0
- Numerical boundary tolerance
- 1e-06
- Eigenvalue coordinates (JSON)
- [[-2,0],[0,0]]
- Linear stability classification
- boundary or numerically indeterminate
Calculation method
Calculation method
Eigenvalue coordinates (JSON)
Continuous: all eigenvalue real parts <0; discrete: all magnitudes <1. Tolerance boundary is indeterminate; no claim of marginal stability without Jordan analysis.
Linear stability classification
Continuous: all eigenvalue real parts <0; discrete: all magnitudes <1. Tolerance boundary is indeterminate; no claim of marginal stability without Jordan analysis.
Symbols and units
- a
- State matrix A
- b
- Convention: 0 continuous, 1 discrete
- c
- Numerical boundary tolerance
Use the units shown. A list keeps the order in which you enter its values. The symbol ^ means “raised to the power of”.
Assumptions & limits
Assumptions & limits
- User-supplied measurements and assumptions; Continuous: all eigenvalue real parts <0; discrete: all magnitudes <1. Tolerance boundary is indeterminate; no claim of marginal stability without Jordan analysis. Supported limits: Finite numeric values bounded to 1e9 magnitude; lists and tables contain 1–100 records unless a stricter bound is stated. Inputs use the units shown. Lists explicitly paired by a method must have matching lengths; independent polynomial coefficient vectors may differ. Respect stated physical, interpolation, policy and computational domain limits. Polynomial degrees are bounded to 6. Higher-degree near-multiple roots with a small derivative relative to coefficient scale are rejected as ill-conditioned; nonconvergent root solves are rejected rather than presented as accurate.
Are these inputs private?
These calculations run in your browser. A shared link contains the values you choose to share. Only questions submitted to the separate AI finder are sent to OpenAI.
Further reading
Background reading; this does not imply endorsement or independent review of SumFizz.