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  "body": "\n## Summary\n\nA band matrix is a matrix whose nonzero entries all lie in a band around the main diagonal.\nThe widths of the band below and above the diagonal are the lower and upper bandwidths.\n[[Diagonal|044JNC7ZAA]], [[tridiagonal|DARX1KZRHZ]] and [[triangular|GTG8MJGDKC]] matrices are special band matrices.\nAlgorithms such as Gaussian elimination without pivoting keep the band, so systems with narrow band matrices are cheap to store and to solve.\n\n## Explanations\n\n### L1 human\n\nMany problems link each unknown only to a few nearby unknowns, such as points on a line or a grid.\nThe matrix of such a problem has zeros everywhere except in a strip along the diagonal.\nFor example, a $5 \\times 5$ matrix with nonzero entries only where the row and column numbers differ by at most $2$ is a band matrix of bandwidth $2$.\nOne only needs to store the strip, which saves memory and time when the matrix is large.\n",
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