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  "body": "\n## Summary\n\nA totally positive matrix is a real matrix all of whose [[minors|0BT9BYWVRY]] are positive.\nWhen the minors are only required to be nonnegative, the matrix is called totally nonnegative.\nTotally positive matrices have strong spectral properties: a square one has only positive, distinct eigenvalues.\nThey occur in approximation theory, in probability, in combinatorics and in the study of oscillating mechanical systems.\n\n## Explanations\n\n### L1 human\n\nEvery entry of a matrix is a $1 \\times 1$ minor, and determinants of larger square pieces are larger minors.\nA totally positive matrix is one where every such determinant, of every size and position, is positive.\nFor example, $\\begin{pmatrix} 1 \u0026 1 \\\\ 1 \u0026 2 \\end{pmatrix}$ has positive entries and determinant $1$, so it is totally positive.\nThe condition is much stronger than having positive entries: $\\begin{pmatrix} 1 \u0026 2 \\\\ 2 \u0026 1 \\end{pmatrix}$ has positive entries but determinant $-3$.\n",
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