On the Reduced Minimum Modulus of Projections and the Angle between Two Subspaces

Let M and N be nonzero subspaces of a Hilbert space H,and PM and PN denote the orthogonal projections on M and N,respectively.In this note,an exact representation of the angle and the minimum gap of M and N is obtained.In addition,we study relations between the angle,the minimum gap of two subspaces M and N,and the reduced minimum modulus of(I-PN)PM.