For ten points, identify this property, which is possessed by any matrix which is row-equivalent to the identity matrix and whose eigenvalues are nonzero.
Picard groups are groups of equivalence classes of fractional ideals with this property. If T is a linear operator on a Hilbert space, then the spectrum of T is the set of λ such that T − λI does not have this property on all of the Hilbert space. Maps with this property comprise the elements of the holonomy group of a Riemann manifold, and a square matrix has this property if it has as many   pivot positions as columns or rows. A knot is said to have this property if it can be transformed into a copy of itself with the orientation reversed. For ten points, identify this property, which is possessed by any matrix which is row-equivalent to the identity matrix and whose eigenvalues are nonzero.
Picard groups are groups of equivalence classes of fractional ideals with this property.
invertibility [accept word forms]