transformation

In linear algebra, linear transformations can be represented by matrices. If



T


{\displaystyle T}
is a linear transformation mapping





R


n




{\displaystyle \mathbb {R} ^{n}}
to





R


m




{\displaystyle \mathbb {R} ^{m}}
and






x
→





{\displaystyle {\vec {x}}}
is a column vector with



n


{\displaystyle n}
entries, then




T
(



x
→



)
=

A




x
→





{\displaystyle T({\vec {x}})=\mathbf {A} {\vec {x}}}
for some



m
×
n


{\displaystyle m\times n}
matrix



A


{\displaystyle A}
, called the transformation matrix of



T


{\displaystyle T}
. Note that



A


{\displaystyle A}
has



m


{\displaystyle m}
rows and



n


{\displaystyle n}
columns, whereas the transformation



T


{\displaystyle T}
is from





R


n




{\displaystyle \mathbb {R} ^{n}}
to





R


m




{\displaystyle \mathbb {R} ^{m}}
. There are alternative expressions of transformation matrices involving row vectors that are preferred by some authors.

View More On Wikipedia.org