Does it mathematically make sense for a number to be added to a vector (or matrix for that matter)? When I put 4 + [ 1 , 2 , 3 ] into Wolfram Alpha it gives me [ 5 , 6 , 7 ], i.e. the number is added to each item, but this doesn't seem correct to me as I would have thought that the number would just be added to the 1st item of the vector - or is neither correct?

Question

Does it mathematically make sense for a number to be added to a vector (or matrix for that matter)? When I put   4  +  [  1  ,  2  ,  3  ] into Wolfram Alpha it gives me   [  5  ,  6  ,  7  ], i.e. the number is added to each item, but this doesn&#039;t seem correct to me as I would have thought that the number would just be added to the 1st item of the vector - or is neither correct?

Urijah Hahn · Accepted Answer

Formally speaking, if   x  ∈      R   and             v      →        =  (      v    k        )          k      =      1        n    ∈            R        n  , for n&amp;gt;1, then   x  +            v      →        is not a defined operation, unlike   x            v      →       , which is defined to be component-wise multiplication, i.e.,  x            v      →        :=  (  x      v    k        )          k      =      1        n    .Thus, you can define the addition to be whatever you like to make life easier and notation simpler.In many computer implementations, e.g. Mathematica or Python&#039;s numpy, you will find the notation  x  +            v      →        :=  x            1      →        +            v      →        =  (  x  +      v    k        )          k      =      1        n    ,which sometimes serves as a useful notational shorthand.