[線代] 對稱正定矩陣的奇異值比較

[playmypig (玩我豬)]

Let A, B be two symmetric positive definite matrices with eigenvalues >= 1.

Prove that the k-th singular value of BA is greater than or equal to

the k-th singular value of A.

用計算機很容易就驗證出來了, 但不知道怎樣下手去證.

故向各位版友請益.

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→ kuromu      : (Ax)^T(B^2-I)Ax ?
→ playmypig   : k大,可以詳細點嗎?