Is it possible to find a rectangular matrix U such that we can write the nxn identity matrix as where * denotes transpose complex conjugation and that where denotes the mxm identity matrix
Is it possible to find a rectangular matrix U such that we can write the nxn identity matrix as where * denotes transpose complex conjugation and that where denotes the mxm identity matrix
What is the context? Can you not just set m=n=1...(although...what do you mean by complex conjugation w.r.t. matrices?)
* is taking the transpose of the matrix and taking the complex conjugate of the entries of the matrix, for the case where n=m, it is trivial, but what about the case?
Is it possible to find a rectangular matrix U such that we can write the nxn identity matrix as where * denotes transpose complex conjugation and that where denotes the mxm identity matrix
Not unless m=m, because U*U and UU* have the same rank, but has rank n and has rank m.