A totally positive matrix is a square matrix whose every minor, the determinant
of a square submatrix, is positive.
For instance, a 
matrix is totally positive iff its
determinant and all its entries are positive.
Replacing strict positivity of every minor by nonnegativity
gives a totally nonnegative matrix.
See also
Generalized Vandermonde
Matrix,
Totally Nonnegative Matrix
Portions of this entry contributed by Todd
Rowland
Explore with Wolfram|Alpha
References
Gantmacher, F. R. The Theory of Matrices, Vol. 2. Providence, RI: AMS Chelsea, 2000.Referenced
on Wolfram|Alpha
Totally Positive Matrix
Cite this as:
Weisstein, Eric W., with contributions by Todd Rowland. "Totally Positive Matrix." From MathWorld--A
Wolfram Resource. https://mathworld.wolfram.com/TotallyPositiveMatrix.html
Subject classifications
