The Eckart-Young Theorem. Suppose a matrix A∈Rm×n has an SVD-decomposition A=UΣVT . Let k<r=rank(A) and truncated matrix Ak=∑i=1kσiuiviT, then, for any matrix B of rank k , the minimal error is achieved with Ak : minrank(B)=k||A−B||2=||A−Ak||2=σk+1. Th...
On a theorem stated by eckart and youngProof is given for a theorem stated but not proved by Eckart and Young in 1936, which has assumed considerable importance in the theory of lower-rank approximations to matrices, particularly in factor analysis.doi:10.1007/BF02289573Richard Johnson...
We present a simple proof of the following theorem of Wiegmann, but in principle given earlier by Eckart and Young: THEOREM If {Ai) is a set of complex r – s matrices such thatA A andA A are Hermitian for all i andj, then there exist unitary matrices P and Q such that for each...
theoryfortheEckart-Young- Mirskytheoremandtheconstrained total leastsquaresproblem ’ MushengWei DepartmentofMathematics,EastChinaNormalUniversity,Shanghai200062, People’sRepublicofChina Received 2July1991;receivedinrevisedform4February1998;accepted12February1998 ...
AGeneralizationoftheEckart-Young-MirskyMatrixApproximationTheoremG.H.Golub*DepartmentofComputerScienceStanfordUniversityStanford,Cali..
Proof of the Wigner-Eckart TheoremSpringer Berlin Heidelbergdoi:10.1007/978-3-540-70727-1_21