問題詳情

10. Let A be an n x n matrix whose (i, j) component is aij. Let f be a real-valued function defined on A.Let  ∇Af( A ) be the gradient of f( A ) with respect to A； ∇Af( A )is delined as an n x n matrix whose (i, j) entry is

. Let B and C be n x n matrices. Which of the following statements are true?
(A) If f( A ) = tr(AB), then ∇Af( A )= B.
(B) If f( A ) = tr(AB), then ∇Af( A ) = BT.
(C) If f( A ) = tr(AATC), then ∇Af( A ) = CA + CTAT.
(D) If f( A ) == tr(AATC), then ∇Af(  A  ) = CA + CAT.
(E) None of the above.

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