Fuglede−Kadison determinant

In mathematics, the Fuglede−Kadison determinant of an invertible operator in a finite factor is a positive real number associated with it. It defines a multiplicative homomorphism from the set of invertible operators to the set of positive real numbers. The Fuglede−Kadison determinant of an operator ${\displaystyle A}$ is often denoted by ${\displaystyle \Delta (A)}$.

For a matrix ${\displaystyle A}$ in ${\displaystyle M_{n}(\mathbb {C} )}$, ${\displaystyle \Delta (A)=\left|\det(A)\right|^{1/n}}$ which is the normalized form of the absolute value of the determinant of ${\displaystyle A}$.