Nullspace Property for Optimality of Minimum Frame Angle Under Invertible Linear Operators

Frames with a large minimum angle between any two distinct frame vectors are desirable in many present day applications. For unit norm frame, the absolute value of cosine is also known as coherence. Two frames equivalent if one can be obtained from other via left action an invertible linear operator. Frame angles change under Most existing works solve different optimization problems to find optimal operator that maximizes minimal (in words, minimizes coherence). In work, nevertheless, we consider question: Is it always possible smaller coherence for given frame?. this paper, derive properties initial ensure strictly larger compared one. It turns out nullspace property certain matrix guarantee such frame. We numerical results support our theoretical claims.