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  "body": "\n## Summary\n\nA normed algebra is an algebra over the real or complex numbers with a norm that is compatible with the product.\nThe norm of a product is at most the product of the norms.\nThis inequality makes multiplication continuous and lets power series of elements converge.\nA complete normed algebra is a Banach algebra.\nAlgebras of bounded operators and of bounded continuous functions are the main examples.\n\n## Explanations\n\n### L1 human\n\nA normed algebra is a space where one can add, scale and multiply elements, and also measure their size.\nThe rule $\\norm{xy} \\le \\norm{x} \\norm{y}$ says that multiplying cannot blow sizes up more than the sizes themselves allow.\nFor square matrices with the operator norm, this rule says that applying two maps in a row stretches vectors by at most the product of the two stretch factors.\n",
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