Condition number

Tags

• algebra
• algebra formula
• linear
• norms
• norms conditioning

Detail

Conditions

• The formula \|A\|\|A^{-1}\| requires A to be invertible.
• For a singular matrix, the condition number is considered infinite in this context.

Related formulas

• Related

  Invertibility criterion

  $$A\text{ invertible}\iff\det(A)\ne0$$
  Open formulaOpen in section

• Related

  Inverse of a 2×2 matrix

  $$A^{-1}=\frac1{ad-bc}\begin{pmatrix}d&-b\\-c&a\end{pmatrix}$$
  Open formulaOpen in section

• Related

  Induced matrix norm

  $$\|A\|_p = \max_{\mathbf x\neq\mathbf0} \frac{\|A\mathbf x\|_p}{\|\mathbf x\|_p}.$$
  Open formulaOpen in section

• Related

  Spectral norm

  $$\|A\|_2 = \sigma_{\max}(A).$$
  Open formulaOpen in section

• Related

  SVD

  $$A=U\Sigma V^T$$
  Open formulaOpen in section