MATRIX DECOMPOSITION DEVICE, MATRIX DECOMPOSITION METHOD AND PROGRAM

摘要

PROBLEM TO BE SOLVED: To decompose a matrix into a block diagonal matrix or a matrix convertible thereto only by operations of a matrix smaller size than the above matrix. SOLUTION: From a matrix G, submatrices G(11), G(22) are extracted. The eigenvalues y(1), ..., y(d) and eigenvectors V(11), ..., V(1d), ..., V(21), ..., V(2d) of the matrix product G(11)**G(11), ..., G(22) * G(22)*are determined. Y(1)=diag(√y(1), ..., √y(d)), Y(2)=diag(i√(1-y(1))), ..., i√(1-y(d)), P(1)=(ei*θ(11)* V(11), ..., ei*θ(1d)* V(1d)), P(2)=(ei*θ(21)* V(21), ..., ei *θ(2d)* V(2d)), K(1)P(1)=(ei*ϕ(11)* W(11), ..., ei*ϕ(1d)* W(1d)), K(2)P(2)=(ei*ϕ(21)* W(21), ..., ei*ϕ(2d)* W(2d)) are generated. COPYRIGHT: (C)2011,JPO&INPIT