Matrix Representation of Linear Operators
Submitted by Structure on Fri, 11/16/2007 - 08:54.
Let us consider a k-vector space morphism of vector space between two finite dimensional k-vector spaces.over a field k. We shall call such an object linear transform or linear operator.
So let be two k-vector and
the set of k-linear operators from
to
. If
then
we have
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Let be a basis in
and
be a basis in
. For all
there are
such as
.
Now
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But if we write we have
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and , as form a basis in
we have for all i from 1 to m
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Let be We shall call
the matrix representation of
in the two basis
and write
Let vectors in
written in column form.
then relation
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has an analog
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deduced by (1)