linear trans.

[angel]

hi,

Could someone please show me how these are a linear transformation please:

1) T(s u + r V)
s and r are scalars and u and v are vectors.

2) composite function:
u : v

thanks

[matt grime]

that would depend on what T is, and what : means, 'composite function' not being something standard, at least not in any useful sense here.

[HallsofIvy]

The questions as stated make no sense.

T(su+ rv)= sT(u)+ rT(v) is the definition of "linear transformation".

If you have one linear transformation T from, say, vector space U to vector space V, and another linear transformation S from V to vector space W, then it is true that
the composition S(T), from U to W, is a linear transformation. Is that what you mean?