Shear is the translation along
an axis (say, **X axis**) by an amount that increases linearly with
another axis (**Y**). It produces shape distortions as if
objects were composed of layers that are caused to slide
over each other [].

Shear transformations are very useful in creating italic letters and slanted letters from regular letters.

where **h** is the negative or positive fraction of **Y**
coordinate of **P** to be added to the **X** coordinate.
can be any real number.

The matrix of form of shear in x-direction is given by

Combining the shear in **X** and **Y** directions,

where **g** is a non-zero fraction of to be added to the
**Y** coordinate.

The general matrix form of shear is

Shear will reduce to a pure shear in the y-direction,
when **h=0**.

The inverse of Shear is given by

- If , then shear along
**X**direction of the point is obtained by substituting these values in (0.3).Shear in

**Y**direction is - Consider a square of side = 2. Show the effect of shear when (1)

Shear along any pair of axes is proportional to the third axis.
For instance, to shear along **z** in 3D, **x** and **y** values are altered
by an amount proportional to the value of **z**, leaving **z** unchanged.
Let , is the shear due to **z** along **x** and
**y** directions respectively and are real values.
Then the matrix representation is

Shear for **x** , **y** axis is similar to that of **z**.
The general form of shear is given by