is a linear mapping or a linear operator if it verifies the
following properties:

1.

.

2.

.

Proposition 6.1.2
Let V and W be two vector spaces. A mapping

is a linear mapping if, and only if,
it verifies the following property:

Proposition 6.1.3
Let U,V,W be three vector spaces with respective dimension m,n,p, in which bases are given.
Let
and
be two linear mappings. Then
is a linear mapping.