Question: Let L1: U v1 and L2: U V2 be linear maps between inner product spaces, with V1, V2 not necessarily the same. Let

Let L1: U → v1 and L2: U → V2 be linear maps between inner product spaces, with V1, V2 not necessarily the same. Let K1 = L1* ○ L1, K2 = L2* ○ L2. Show that the sum K = K1 + K2 can be written as a self-adjoint combination K = L* ○ L for some linear operator L.

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