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  "body": "\n## Summary\n\nA matrix norm is a [[norm|0V2WP9B1MF]] on a space of matrices, often required to be submultiplicative: $\\norm{AB} \\le \\norm{A} \\norm{B}$.\nIt measures the size of a matrix and so the size of errors and perturbations in matrix computations.\nThe main examples are the [[operator norms|06EKW1AKXF]] induced by vector norms and the [[Frobenius norm|JT8Q204E4R]].\nEvery submultiplicative matrix norm bounds the [[spectral radius|9V7YQA85PC]] from above.\n\n## Explanations\n\n### L1 human\n\nA matrix norm gives one nonnegative number that says how big a matrix is.\nOne way is to ask how much the matrix can stretch a vector of length $1$.\nAnother way is to treat the matrix as a long list of numbers and take its usual length.\nFor the diagonal matrix with entries $3$ and $4$, the largest stretch is $4$, and the length of the list $(3, 0, 0, 4)$ is $5$.\n",
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