V = P2 : p, q = a0b0 − a1b1 + a2b2, with p(x) = a0 + a1x + a2x 2 , q(x) = b0 + b1x + b2x 2 , x ∈ R.
Is this an inner product on the given vector space ?
2026-05-02 09:16:56.1777713416
Determine if the following is an inner product on the given vector space:
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No , positivity axiom does not hold.
Counter example : p(x) = 1 +2x + x^2
Hence < p , p > = -2