A square matrix is said to be totally positive if the determinant of any square submatrix,
including the minors, is positive. For instance, any 
matrix whose determinant is positive
and whose entries are positive is a totally positive matrix.
Totally Positive Matrix
See also
Generalized Vandermonde MatrixThis entry contributed by Todd Rowland
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References
Gantmacher, F. R. The Theory of Matrices, Vol. 2. Providence, RI: AMS Chelsea, 2000.Referenced on Wolfram|Alpha
Totally Positive MatrixCite this as:
Rowland, Todd. "Totally Positive Matrix." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/TotallyPositiveMatrix.html