Question

State whether True or False.
For every abstract nonzero vector space 

V

 over 

R

, there exists a function 

⟨⋅,⋅⟩:V×V→R

 such that 

(V,⟨⋅,⋅⟩)

 is an inner product space.

True

 

False

​

Answer 1

Answer:

True is the answer

Step-by-step explanation:

I hope this Will help you .

Answer 2

Answer:

It is true that For every abstract nonzero vector space V over R, there exists a function ⟨⋅,⋅⟩:V×V→R such that (V,⟨⋅,⋅⟩) is an inner product space.

Concept:

An inner product space in mathematics is a real vector space or a complex vector space with an inner product operation. A scalar is the inner product of two vectors in the space, and it is frequently represented by angle brackets, like <a | b>. Inner products enable intuitive geometric concepts like lengths, angles, and orthogonality (zero inner product) of vectors to be defined formally. Inner product spaces, in which the inner product is the dot product or scalar product of Cartesian coordinates, generalize Euclidean vector spaces. Functional analysis frequently makes use of infinite dimensional inner product spaces. Unitary spaces are a term that is occasionally used to describe inner product spaces over the field of complex numbers.

Hence, The answer is that It is true that For every abstract nonzero vector space V over R, there exists a function ⟨⋅,⋅⟩:V×V→R such that (V,⟨⋅,⋅⟩) is an inner product space.

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