CALCULATOR
Positive Diagonal 2×2 Spectral Condition Number Calculator
Positive Diagonal 2×2 Spectral Condition Number Calculator — change the supplied values to calculate positive diagonal 2×2 spectral condition number.
Only strictly positive diagonal 2×2 matrices; off-diagonal entries fixed at zero. No general matrix condition estimate.
Accepted inputs: A: 0.01 to 100 number; D: 0.01 to 100 number.
How the calculation works
κ₂(diag(a,d))=max(a,d)/min(a,d)
Positive diagonal matrices have singular values a,d. The 2-norm condition number is their largest to smallest ratio.
Worked example
With a 2 number, d 8 number, positive diagonal 2×2 spectral condition number is 4 number.
Assumptions and limits
Only strictly positive diagonal 2×2 matrices; off-diagonal entries fixed at zero. No general matrix condition estimate.