My Math Forum simple true/false regarding inner product spaces

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 November 8th, 2017, 07:58 AM #1 Newbie   Joined: Aug 2017 From: mathmatistan Posts: 9 Thanks: 0 simple true/false regarding inner product spaces hello, could you check if i marked the correct answers? a)let v=M_{nxn}^R and let A, B \in V, (A,B) = tr(BA) defines an inner product on V. (incorrect, it does not and when i tried to use various inputs got also wrong answer. just not true) b)let V=R^2 and let u=(x_1,x_2) and v=(y_1,y_2) \in V. (u,v)=x_1+y_1 defines an inner product in V (only if x_2 and y_2 are equal to zero, does it considered to be a valid claim or not?) (it's american, but i want to be sure that i got it right so if i wrote something wrong please correct me). thank you very much
November 28th, 2017, 04:55 AM   #2
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Quote:
 Originally Posted by mathsnoob hello, could you check if i marked the correct answers? a)let v=M_{nxn}^R and let A, B \in V, (A,B) = tr(BA) defines an inner product on V. (incorrect, it does not and when i tried to use various inputs got also wrong answer. just not true)
I'm not sure what you mean by "tried to use various inputs". "Various inputs in what? You should say exactly what requirements for an inner product are violated.

Quote:
 b)let V=R^2 and let u=(x_1,x_2) and v=(y_1,y_2) \in V. (u,v)=x_1+y_1 defines an inner product in V (only if x_2 and y_2 are equal to zero, does it considered to be a valid claim or not?)
The problem says "let V= R^2" so this has to apply to all vectors in R^2, not just those with first number 0. Actually, even so, x+ y is not an inner product because (x, x) may be negative.

Quote:
 (it's american, but i want to be sure that i got it right so if i wrote something wrong please correct me). thank you very much

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