<svg
  viewBox="-40 0 150 100"
  xmlns="http://www.w3.org/2000/svg"
  xmlns:xlink="http://www.w3.org/1999/xlink">
  <g
    fill="grey"
    transform="rotate(-10 50 100)
               translate(-36 45.5)
               skewX(40)
               scale(1 0.5)">
    <path
      id="heart"
      d="M 10,30 A 20,20 0,0,1 50,30 A 20,20 0,0,1 90,30 Q 90,60 50,90 Q 10,60 10,30 z" />
  </g>

  <use xlink:href="#heart" fill="none" stroke="red" />
</svg>

In SVG 1.1, only these 16 elements were allowed to use it: <a>, <circle>, <clipPath>, <defs>, <ellipse>, <foreignObject>, <g>, <image>, <line>, <path>, <polygon>, <polyline>, <rect>, <switch>, <text>, and <use>).

Also, as a legacy from SVG 1.1, <linearGradient> and <radialGradient> support the gradientTransform attribute, and <pattern> supports the patternTransform attribute, both of which act exactly like the transform attribute.

The following transform functions can be used by the transform attribute <transform-list>

The matrix(<a> <b> <c> <d> <e> <f>) transform function specifies a transformation in the form of a transformation matrix of six values. matrix(a,b,c,d,e,f) is equivalent to applying the transformation matrix: $$\begin{pmatrix} a & c & e \ b & d & f \ 0 & 0 & 1 \end{pmatrix}$$ which maps coordinates from a previous coordinate system into a new coordinate system by the following matrix equalities: $$\begin{pmatrix} x_{\mathrm{newCoordSys}} \ y_{\mathrm{newCoordSys}} \ 1 \end{pmatrix} = \begin{pmatrix} a & c & e \ b & d & f \ 0 & 0 & 1 \end{pmatrix} \begin{pmatrix} x_{\mathrm{prevCoordSys}} \ y_{\mathrm{prevCoordSys}} \ 1 \end{pmatrix} = \begin{pmatrix} a x_{\mathrm{prevCoordSys}} + c y_{\mathrm{prevCoordSys}} + e \ b x_{\mathrm{prevCoordSys}} + d y_{\mathrm{prevCoordSys}} + f \ 1 \end{pmatrix}$$

Example

<svg viewBox="0 0 200 200" xmlns="http://www.w3.org/2000/svg">
  <rect x="10" y="10" width="30" height="20" fill="green" />

  <!--
  In the following example we are applying the matrix:
  [a c e]    [3 -1 30]
  [b d f] => [1  3 40]
  [0 0 1]    [0  0  1]

  which transform the rectangle as such:

  top left corner: oldX=10 oldY=10
  newX = a * oldX + c * oldY + e = 3 * 10 - 1 * 10 + 30 = 50
  newY = b * oldX + d * oldY + f = 1 * 10 + 3 * 10 + 40 = 80

  top right corner: oldX=40 oldY=10
  newX = a * oldX + c * oldY + e = 3 * 40 - 1 * 10 + 30 = 140
  newY = b * oldX + d * oldY + f = 1 * 40 + 3 * 10 + 40 = 110

  bottom left corner: oldX=10 oldY=30
  newX = a * oldX + c * oldY + e = 3 * 10 - 1 * 30 + 30 = 30
  newY = b * oldX + d * oldY + f = 1 * 10 + 3 * 30 + 40 = 140

  bottom right corner: oldX=40 oldY=30
  newX = a * oldX + c * oldY + e = 3 * 40 - 1 * 30 + 30 = 120
  newY = b * oldX + d * oldY + f = 1 * 40 + 3 * 30 + 40 = 170
  -->
  <rect
    x="10"
    y="10"
    width="30"
    height="20"
    fill="red"
    transform="matrix(3 1 -1 3 30 40)" />
</svg>

The translate(<x> [<y>]) transform function moves the object by x and y. If y is not provided, it is assumed to be 0.

In other words:

xnew = xold + <x>
ynew = yold + <y>

Example

<svg viewBox="0 0 100 100" xmlns="http://www.w3.org/2000/svg">
  <!-- No translation -->
  <rect x="5" y="5" width="40" height="40" fill="green" />

  <!-- Horizontal translation -->
  <rect
    x="5"
    y="5"
    width="40"
    height="40"
    fill="blue"
    transform="translate(50)" />

  <!-- Vertical translation -->
  <rect
    x="5"
    y="5"
    width="40"
    height="40"
    fill="red"
    transform="translate(0 50)" />

  <!-- Both horizontal and vertical translation -->
  <rect
    x="5"
    y="5"
    width="40"
    height="40"
    fill="yellow"
    transform="translate(50 50)" />
</svg>

The scale(<x> [<y>]) transform function specifies a scale operation by x and y. If y is not provided, it is assumed to be equal to x.

Example

<svg viewBox="-50 -50 100 100" xmlns="http://www.w3.org/2000/svg">
  <!-- uniform scale -->
  <circle cx="0" cy="0" r="10" fill="red" transform="scale(4)" />

  <!-- vertical scale -->
  <circle cx="0" cy="0" r="10" fill="yellow" transform="scale(1, 4)" />

  <!-- horizontal scale -->
  <circle cx="0" cy="0" r="10" fill="pink" transform="scale(4, 1)" />

  <!-- No scale -->
  <circle cx="0" cy="0" r="10" fill="black" />
</svg>

The rotate(<a> [<x> <y>]) transform function specifies a rotation by a degrees about a given point. If optional parameters x and y are not supplied, the rotation is about the origin of the current user coordinate system. If optional parameters x and y are supplied, the rotation is about the point (x, y).

Example

<svg viewBox="-12 -2 34 14" xmlns="http://www.w3.org/2000/svg">
  <rect x="0" y="0" width="10" height="10" />

  <!-- rotation is done around the point 0,0 -->
  <rect x="0" y="0" width="10" height="10" fill="red" transform="rotate(100)" />

  <!-- rotation is done around the point 10,10 -->
  <rect
    x="0"
    y="0"
    width="10"
    height="10"
    fill="green"
    transform="rotate(100, 10, 10)" />
</svg>

The skewX(<a>) transform function specifies a skew transformation along the x axis by a degrees.

Example

<svg viewBox="-5 -5 10 10" xmlns="http://www.w3.org/2000/svg">
  <rect x="-3" y="-3" width="6" height="6" />

  <rect x="-3" y="-3" width="6" height="6" fill="red" transform="skewX(30)" />
</svg>

The skewY(<a>) transform function specifies a skew transformation along the y axis by a degrees.

Example

<svg viewBox="-5 -5 10 10" xmlns="http://www.w3.org/2000/svg">
  <rect x="-3" y="-3" width="6" height="6" />

  <rect x="-3" y="-3" width="6" height="6" fill="red" transform="skewY(30)" />
</svg>