Question

can a vector be squared ?

Answer 1

Yes, but it'll be the square of its magnitude

Answer 2

\[ v^2 = \vec v \cdot \vec v\]

Answer 3

You can square the individual components, or find its dot product with itself...but just "squaring a vector" doesn't have a whole lot of meaning.

Answer 4

say the vector is 1 by n

Answer 5

so that's a no?

Answer 6

only two vector product are defined ... dot and cross
if you take dot product, you will square of magnitude
if you take cross product you will end up zero.

Answer 7

how did you get zero for the cross product?

Answer 8

You can define what ever algebraic structure you please (group, ring, field) on vectors and define the operation(s) as long as they satisfy the structure axioms...but there is no common multiplication for vectors.

Answer 9

is multiplying by the duel vector like squaring the vector/?