## What are the dimensions of a vector?

## How many dimensions does a vector have?

- so the general vector a is Vectors add, subtract and scale as in
**three dimensions**. The dot product of Euclidean three-dimensional space generalizes to four dimensions as It can be used to calculate the norm or length of a vector,

## Why is the dimension of the vector space?

- The dimension of a vector space V, denoted dim(V), is the number of vectors in a basis for V . We deﬁne the dimension of the vector space containing only the zero vector 0 to be 0. In a sense, the dimension of a vector space tells us how many vectors are needed to "build" the space , thus gives us a way to compare the relative sizes of the ...

## What are vector spaces?

- A vector space (also called a
**linear space)**is a**collection of objects called vectors**, which may be added together and multiplied ("scaled") by numbers, called scalars. Scalars are often taken to be real numbers, but there are also vector spaces with**scalar multiplication**by complex numbers, rational numbers, or generally any field.

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