Implements DetRootN.


class picos.expressions.exp_detrootn.DetRootN(x)[source]

Bases: picos.expressions.expression.Expression

The n-th root of the determinant of an n\times n matrix.


For an n \times n positive semidefinite hermitian matrix X, this is

\sqrt[n]{\det X}.


When you pose a lower bound on the n-th root of a determinant of the matrix X, then PICOS enforces positive semidefiniteness X \succeq 0 through an auxiliary constraint during solution search.


Return a constraint that the expression is lower-bounded.


Construct a DetRootN.


x (ComplexAffineExpression) – The matrix concerned. Must be hermitian by definition.


Denote multiplication with another expression on the right.


Denote multiplication with another expression on the left.

property n

Diagonal length of x.

property x

The matrix concerned.