Editing Transformation matrix (section)

===Stretching===

A stretch in the ''xy''-plane is a linear transformation which enlarges all distances in a particular direction by a constant factor but does not affect distances in the perpendicular direction. We only consider stretches along the x-axis and y-axis. A stretch along the x-axis has the form {{math|1=<var>x'</var> = <var>kx</var>}}; {{math|1=<var>y'</var> = <var>y</var>}} for some positive constant {{mvar|k}}. (Note that if {{math|1=<var>k</var> &gt; 1}}, then this really is a "stretch"; if {{math|1=<var>k</var> &lt; 1}}, it is technically a "compression", but we still call it a stretch. Also, if {{math|1=<var>k</var> = 1}}, then the transformation is an identity, i.e. it has no effect.)

The matrix associated with a stretch by a factor {{mvar|k}} along the x-axis is given by:
<math display="block">\begin{bmatrix} k &  0 \\ 0 & 1 \end{bmatrix} </math>

Similarly, a stretch by a factor <var>k</var> along the y-axis has the form {{math|1=<var>x'</var> = <var>x</var>}}; {{math|1=<var>y'</var> = <var>ky</var>}}, so the matrix associated with this transformation is
<math display="block">\begin{bmatrix} 1 &  0 \\ 0 & k \end{bmatrix} </math>