Suppose (v w), and (v, w)2 are two inner products on the same vector space V For which or R is the linear combination (v w) a(v, w), (v, w)2 a legitimate inner product Hint The case when a, 0 is easy However, some negative values are also permitted, and your task is to decide which ...

First since vw is easily shown to be bilinear and symmetric the only issue is posit ...

Suppose (v. w), and (v, w)2 are two inner products on the same vector space V. For

Question:

Suppose (v. w), and (v, w)2 are two inner products on the same vector space V. For which or. α β ∈ R is the linear combination (v. w) = a(v, w), + β (v, w)2 a legitimate inner product? Hint: The case when a, β ≥ 0 is easy. However, some negative values are also permitted, and your task is to decide which.