A totally positive matrix is a square matrix for which 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:
Weisstein, Eric W., with contributions by Todd Rowland. "Totally Positive Matrix." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/TotallyPositiveMatrix.html