In mathematics, a totally positive matrix is a square matrix in which all the minors are positive: that is, the determinant of every square submatrix is a positive number.
A symmetric totally positive matrix is therefore also positive-definite.
A totally non-negative matrix is defined similarly, except that all the minors must be non-negative (positive or zero).
where: Then A is a totally positive matrix if:[2] for all submatrices
Topics which historically led to the development of the theory of total positivity include the study of:[2] For example, a Vandermonde matrix whose nodes are positive and increasing is a totally positive matrix.
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