Difference between a vector in RR_1 and a scalar Many people say that they are the same, even I can't find much difference in them except that a vector/ matrix can be multiplied by any scalar, but to multiply it with a vector in RR1 the vector or matrix should be of the order 1 xx n. What's and why is there a difference in this case?

Jadon Johnson

Jadon Johnson

Answered question

2022-11-17

Difference between a vector in R 1 and a scalar
Many people say that they are the same, even I can't find much difference in them except that a vector/ matrix can be multiplied by any scalar, but to multiply it with a vector in R 1 the vector or matrix should be of the order 1 × n. What's and why is there a difference in this case?

Answer & Explanation

dilettato5t1

dilettato5t1

Beginner2022-11-18Added 25 answers

Referring to formal definitions, the main difference is that:
When you consider R as a field, the multiplication is an internal operation. That is maps an ordered pair ( x , y ) R 2 to z = x y R
When you consider V = R as a one-dimensional vector space, then the multiplication is formally a scalar multiplication defined between two distinct objects: the field R and V.

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