To " complexify " a space means extending ordinary scalar multiplication of vectors by real numbers to scalar multiplication by complex numbers.
22.
On this underlying set one defines addition and scalar multiplication pointwise, and " multiplication " in the incidence algebra is a convolution defined by
23.
The "'left scalar multiplication "'of a matrix with a scalar gives another matrix of the same size as.
24.
In addition, there is a natural action of \ mathbb R _ { > 0 } on cv _ n by scalar multiplication.
25.
For example, the inversion; since it is scalar multiplication by " 1, it is clear that it commutes with any linear transformation ).
26.
With the pointwise addition and scalar multiplication of sections, " F " ( " U " ) becomes itself a real vector space.
27.
M�bius scalar multiplication coincides with Einstein scalar multiplication ( see section above ) and this stems from M�bius addition and Einstein addition coinciding for vectors that are parallel.
28.
M�bius scalar multiplication coincides with Einstein scalar multiplication ( see section above ) and this stems from M�bius addition and Einstein addition coinciding for vectors that are parallel.
29.
The coordinate space may then be interpreted as the space of all column vectors, or all row vectors with the ordinary matrix operations of addition and scalar multiplication.
30.
This is homogeneous of degree " d " under scalar multiplication on " V ", and therefore passes to a mapping on the underlying projective spaces.
