= Total nonnegativity of a matrix
= Totally nonnegative matrix
{synonym}
A real rectangular <matrix> is totally nonnegative if every square minor, with row and column indices in increasing order, is nonnegative. A nonnegative bidiagonal <matrix> is totally nonnegative, and products of compatible <totally nonnegative matrices> have the same property by the <Cauchy–Binet formula>. This controls signs of inverse entries and underlies stability and shape-preserving properties of <B-spline> collocation. Total nonnegativity permits zero minors; strict total positivity requires every such minor to be positive.
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