A adjust of works with matrix, likewise called a transition matrix, states the revolution from one vector communication to an additional under a readjust of basis. For example, if

*
and
*
are two vector bases in
*
, and also let
*
_B" /> it is in the collaborates of a vector
*
in communication
*
and
*
_(B^")" /> its coordinates in basis
*
.

You are watching: Change of coordinates matrix from b to c

Write the basis vectors

*
and also
*
for
*
in works with relative to basis
*
as

*
_B" />
*
*
" />

*
_B" />
*
*
." />

This way that

*
*
*

*
*
*

*
" />

which mentions the change of works with of a vector

*
under the change of basis from
*
to
*
via


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