Induced matrix norm

Tags

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

Detail

Intuitive explanation

La norma inducida responde a la pregunta «¿cuál es el vector unitario que más se estira al multiplicar por $A$?». Ese factor máximo es $\|A\|_p$.

Derivation

Worked example

Also known as

• induced matrix norm
• operator norm
• norma de operador
• induced norm formula
• matrix norm induced by vector norm
• norma matricial inducida fórmula

Related topics

• Matrix norms and distances

Related formulas

• Related

  Euclidean norm

  $$\|\mathbf v\|_2=\sqrt{\sum_i v_i^2}$$
  Open formulaOpen in section

• Related

  Matrix 1-norm

  $$\|A\|_1 = \max_j\sum_i|a_{ij}|.$$
  Open formulaOpen in section

• Related

  Matrix infinity norm

  $$\|A\|_\infty = \max_i\sum_j|a_{ij}|.$$
  Open formulaOpen in section

• Related

  Spectral norm

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

• Related

  Condition number

  $$\kappa(A) = \|A\|\,\|A^{-1}\|.$$
  Open formulaOpen in section