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BUILT-IN MATHEMATICA SYMBOL

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ScalingMatrix

gives the matrix corresponding to scaling by a factor

along each coordinate axis.

ScalingMatrix

gives the matrix corresponding to scaling by a factor s along the direction of the vector v.

MORE INFORMATION

ScalingMatrix gives matrices for scaling from the origin.

ScalingMatrix works in any number of dimensions.

EXAMPLES

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Basic Examples (2)

Scaling by factors

, and

along the

, and

directions:

Scaling by a factor

along the direction of the vector

Scaling by factors

, and

along the

, and

directions:

In[1]:=

Out[1]//MatrixForm=

In[2]:=

Out[2]=

Scaling by a factor

along the direction of the vector

In[1]:=

Out[1]//MatrixForm=

In[2]:=

Out[2]=

Scope (3)

Scaling factors can be negative or zero:

Transformation applied to a 2D shape:

Transformation applied to a 3D shape:

Applications (2)

Create an ellipsoid:

Display projection of a 3D graphic:

Properties & Relations (4)

The determinant of ScalingMatrix

is s:

The inverse of ScalingMatrix

is given by ScalingMatrix

The determinant of ScalingMatrix

is given by

The inverse of ScalingMatrix

is given by ScalingMatrix

Neat Examples (1)

Repeated scalings in different directions: