Matrix Norm

Updated 01 Oct 2026

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What it is
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  measures matrix size; an induced norm also bounds how much a matrix can amplify a vector
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Formula
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  $|A|*1=\max_j\sum_i|a*{ij}|$ .
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  $|A|*\infty=\max_i\sum_j|a*{ij}|$ .
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  $|A|_2$ is the largest singular value.
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Property
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  for a compativle induced norm, $|Ax|\le|A||x|$
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Related
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  Condition Number
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  System of Linear Equations

Linked references 2