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  "body": "\n## Summary\n\nA triangular matrix is a square matrix that is either [[upper triangular|0N4XY7Z3NN]] or [[lower triangular|00J3KZP8Y0]].\nAll its entries on one side of the main diagonal are zero.\nLinear systems with a triangular matrix are solved quickly by substitution.\nThe [[determinant of a triangular matrix|0K1KKMFHYH]] is the product of its diagonal entries, and these entries are its eigenvalues.\nMany factorisations, such as LU, QR and the [[Schur decomposition|V1JG4C7R7B]], produce triangular factors.\n\n## Explanations\n\n### L1 human\n\nPicture a square table of numbers cut along its main diagonal.\nA triangular matrix has only zeros in one of the two halves, so its nonzero entries fill a triangle.\nFor example, $\\begin{pmatrix} 1 \u0026 4 \\\\ 0 \u0026 2 \\end{pmatrix}$ is upper triangular and $\\begin{pmatrix} 3 \u0026 0 \\\\ 5 \u0026 1 \\end{pmatrix}$ is lower triangular.\nIn a system with such a matrix, one equation has a single unknown, and each next equation adds only one new unknown.\n",
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