A linear transformation matrix is a mathematical tool for describing linear transformations

Any sequence of these operations in a 2-dimensional plane can be described by one linear transformation matrix of 6 parameters. It can do the following

- Transform a square into a square, a rotated square, a rectangle, a rotated rectangle, a rhomb, a rotated rhomb, a parallellogram or a rotated parallellogram
- Transform a circle into a circle, a rotated circle, an ellipse or a rotated ellipse
- Transform parallel lines into parallel lines.

Because parallel lines stay parallel, a linear transformation matrix can describe a 3D isometric projection, but not a 3D perspective projection.

The transformation of a triangle into another triangle uniquely identifies a linear
transformation matrix (`CADCalcMatrix`

).

Applying a linear transformation matrix with `CADTransform`

is generally more
efficient than a succession of singular operations
(`CADTranslate`

, `CADScale`

, `CADMirror`

, `CADRotate`

and
`CADShear`

).

Objects of type Block insert and Raster image have a linear transformation matrix attached

- because linear transformation matrices are generally very efficient
- because linear transforms on those objects will not touch their original content.

The matrix that doesnâ€™t change anything is called the identity matrix
(`CADIdentityMatrix`

).
A matrix that describes one sequence of the operations scale, rotate and translate
(in that order) is called a standard matrix (`CADStandardMatrix`

).
A matrix that undoes the effect of another matrix is called an inverse matrix
(`CADInvertMatrix`

).

Applying one matrix transformation on another is called a matrix multiplication
(`CADTransformMatrix`

).
The term multiplication is somewhat misleading. When multiplying two numbers, the order of the
two numbers is not important. But when multiplying two matrices the order is important.

**Methods**

`CADIdentityMatrix`

, `CADStandardMatrix`

,
`CADTranslateMatrix`

, `CADRotateMatrix`

, `CADScaleMatrix`

,
`CADMirrorMatrix`

,
`CADShearMatrix`

, `CADTransformMatrix`

, `CADFlipMatrix`

,
`CADStretchMatrix`

,
`CADInvertMatrix`

,
`CADCalcMatrix`

,
`CADGetMatrixPlane`

.