Let A={A_1, A_2,…, A_(n+1)} be a simplex in E^n which its center O of circumscribed sphere is in inside of A. If R and R_i are radiuses of A_i respectively (A_i={A_1, A_2,…, A_(i-1), O, A_(i+1),…,A_(n+1)} ,i=1,2,…...Let A={A_1, A_2,…, A_(n+1)} be a simplex in E^n which its center O of circumscribed sphere is in inside of A. If R and R_i are radiuses of A_i respectively (A_i={A_1, A_2,…, A_(i-1), O, A_(i+1),…,A_(n+1)} ,i=1,2,…,n+1),then we have The equality holds if and only if A is a regular simplex.展开更多
We prove that a CP matrix A having cyclic graph has exactly two minimal rank 1 factorization if det M(A) > 0 and has exactly one minimal rank 1 factorization if detM(A) = 0.
文摘Let A={A_1, A_2,…, A_(n+1)} be a simplex in E^n which its center O of circumscribed sphere is in inside of A. If R and R_i are radiuses of A_i respectively (A_i={A_1, A_2,…, A_(i-1), O, A_(i+1),…,A_(n+1)} ,i=1,2,…,n+1),then we have The equality holds if and only if A is a regular simplex.
文摘We prove that a CP matrix A having cyclic graph has exactly two minimal rank 1 factorization if det M(A) > 0 and has exactly one minimal rank 1 factorization if detM(A) = 0.
