Examples
Examples
Try the starting example
- Real matrix, rows on separate lines
- 3,0 0,1
- Condition norm: 2, 1 or inf
- 2
- Relative singular-value rank threshold
- 1e-12
- Condition estimate or singularity status
- 3
- Effective rank at selected threshold
- 2
- Largest singular value
- 3
- Smallest singular value
- 1
Try another scenario
- Real matrix, rows on separate lines
- 3,0 0,0
- Condition norm: 2, 1 or inf
- 2
- Relative singular-value rank threshold
- 1e-12
- Condition estimate or singularity status
- Singular at chosen tolerance
- Effective rank at selected threshold
- 1
- Largest singular value
- 3
- Smallest singular value
- 0
Calculation method
Calculation method
Condition estimate or singularity status
For norm 2 use largest/smallest singular value. For square full-rank matrices, norms 1 and inf use norm(A)×norm(inverse(A)).
Effective rank at selected threshold
Count singular values greater than largest×relative threshold.
Largest singular value
Largest computed singular value.
Smallest singular value
Smallest computed singular value, including zero.
Symbols and units
- a
- Real matrix, rows on separate lines
- b
- Condition norm: 2, 1 or inf
- c
- Relative singular-value rank threshold
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
- Up to 20×20 finite real matrices. Norm 2 supports rectangular matrices; 1 and inf require square matrices. Rank and singularity status depend explicitly on your supplied relative threshold. Double-precision results are approximate. Numeric tables use 12 significant digits and display components at roundoff scale (32 machine epsilons relative to their row or relevant calculation scale) as zero; scalar diagnostics retain full precision.
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
ml-matrix: numerical decompositions ↗
Background reading; this does not imply endorsement or independent review of SumFizz.