Examples
Examples
Try the starting example
- State matrix A
- [[0,1],[-2,-3]]
- Input matrix B
- [[0],[1]]
- Absolute pivot tolerance
- 1e-06
- Controllability rank (count)
- 2
- State dimension (count)
- 2
- Gaussian pivot-scale ratio diagnostic
- 1
Try another scenario
- State matrix A
- [[0,2],[-2,-3]]
- Input matrix B
- [[0],[1]]
- Absolute pivot tolerance
- 1e-06
- Controllability rank (count)
- 2
- State dimension (count)
- 2
- Gaussian pivot-scale ratio diagnostic
- 2
Calculation method
Calculation method
Controllability rank (count)
Form [B,AB,...,A^(n−1)B]; Gaussian elimination with supplied absolute pivot tolerance; ratio of retained elimination pivots is a scale diagnostic, not a condition number.
State dimension (count)
Form [B,AB,...,A^(n−1)B]; Gaussian elimination with supplied absolute pivot tolerance; ratio of retained elimination pivots is a scale diagnostic, not a condition number.
Gaussian pivot-scale ratio diagnostic
Form [B,AB,...,A^(n−1)B]; Gaussian elimination with supplied absolute pivot tolerance; ratio of retained elimination pivots is a scale diagnostic, not a condition number.
Symbols and units
- a
- State matrix A
- b
- Input matrix B
- c
- Absolute pivot 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; Form [B,AB,...,A^(n−1)B]; Gaussian elimination with supplied absolute pivot tolerance; ratio of retained elimination pivots is a scale diagnostic, not a condition number. 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.
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.