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Let V be a real vector space. Suppose to each pair of vectors u,v ε v

1. What does refers by

2. What does

**there is assigned a real number**, denoted by <u, v>.**This function**is called a inner product on V if it satisfies some axioms.1. What does refers by

**"this function"**? Is it "<u, v>"? If it is then How we can call it's a function?2. What does

**"there is assigned a real number"**suggest? Could someone please explain it to me with examples?
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