問題詳情

【題組】

五、Which of the following statements about matrix factorization is/are true?
(A) If a matrix A is positive definite, then A has "an" LU factorization, A = LU, wherethe diagonal entries of U are positive.
(B) Suppose that a matrix A = QR, where Q is an m x n matrix and R is an n X nmatrix. If the columns of A are linearly independent, then R must be invertible.
(C) Any factorization of a matrix A =

, with matrices U, V square and positivediagonal entries in the matrix D, is called a singular value decomposition of A.
(D) An n x n matrix A is positive definite if and only if A has "a" Cholesky factorizationA =

for some invertible upper triangular matrix R whose diagonal entries areall positive.
(E) None of the above are true.

參考答案

答案：[無官方正解]
難度：計算中-1
書單：沒有書單，新增