Let A, B S n be two symmetric matrices Define the component wise product of A, B, by a matrix C S n with elements C ij A ij B ij , 1 i, j n Show that C is positive semidefinite, provided both A, B are

Question: Let A, B S n be two symmetric matrices. Define the component-wise product of A, B, by a matrix C S n with

Let A, B ∈ Sⁿbe two symmetric matrices. Define the component-wise product of A, B, by a matrix C ∈ Sⁿwith elements C_ij= A_ijB_ij, 1 ≤ i, j ≤ n. Show that C is positive semidefinite, provided both A, B are.

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