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Mathematica > Visualization and Graphics > Computational Geometry > Geometric Transforms >

Built-in Mathematica Symbol

ScalingMatrix

ScalingMatrix[{s_x, s_y, ...}]
gives the matrix corresponding to scaling by a factor s_i along each coordinate axis.

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

Scaling by factors a, b and c along the

and

directions:

Scaling by a factor s along the direction of the vector

Scaling by factors a, b and c along the

and

directions:

Out[1]//MatrixForm=

Scaling by a factor s along the direction of the vector

Out[1]//MatrixForm=

Scaling factors can be negative or zero:

Transformation applied to a 2D shape:

Transformation applied to a 3D shape:

Create an ellipsoid:

Display projection of a 3D graphic:

The determinant of ScalingMatrix[s, v] is s:

The inverse of ScalingMatrix[s, v] is given by ScalingMatrix[1/s, v]:

The determinant of ScalingMatrix[{s₁, ..., s_n}] is given by s₁

s_n :

The inverse of ScalingMatrix[{s₁, ..., s_n}] is given by ScalingMatrix[{1/s₁, ..., 1/s_n}]:

Repeated scalings in different directions: