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  "body": "\n## Summary\n\nA matrix summability method uses an infinite matrix $A = (a_{nk})$ to turn a sequence $(s_k)$ into the weighted sums $\\sum_k a_{nk} s_k$.\nThe method then takes the limit of these sums.\nMost classical [[summability methods|8X25Q4XYMN]], such as [[Cesàro summation|N8ZGG7EW6J]], Nörlund means and Euler summation, are of this kind.\nTheir properties can be read off from the entries of the matrix, as in the [[Silverman–Toeplitz theorem|S4J7SRPXMZ]] and the [[Kojima–Schur theorem|JB8GQBVW6Q]].\n\n## Explanations\n\n### L1 human\n\nEach row of the matrix is a recipe for averaging the terms of the sequence with certain weights.\nRow $n$ produces one number, and the method looks at what these numbers do as $n$ grows.\nThe Cesàro matrix has row $n$ equal to $\\frac{1}{n+1}, \\dots, \\frac{1}{n+1}$ followed by zeros, so it takes plain averages of the first $n + 1$ terms.\nApplied to $1, 0, 1, 0, \\dots$ it gives averages that tend to $\\frac12$.\n",
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