RedCrab Math Tutorial
 



Matrices geometric Reflection and Shear

Geometric operations, like rotating a position vector by a certain angle around some axis, can be achieved by multiplying the vector by an appropriate matrix. This page descript how such matrices are constructed.
 

Matrix Reflection

We will consider a point P with the coordinates (x, y) in a two-dimensional space.
In the two dimensional space we draw the vector as

 
The matrix below produces a reflection of the vector across the X-axis

this results in the formula

 
The following figure shows an example with values in RedCrab Calculator

 
A 3-dimensional reflection of the Y position is achieved by the following formula

To produce reflections in the X- or Z-planes, place a negative sign on the corresponding diagonal elements of the unit matrix.
 

Matrix Shear

The insertion of a non-zero element into a position outside the diagonal of the unit matrix produces a shear distortion of the position vector.
Example:

corresponds to

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Matrices Definition
Matrices Calculation
Matrices & Simultaneous Equations
Matrices Determinants
Row Operations of Matrices
Matrices and Geometry, Reflection
Matrices and Geometry, Rotation
   


           
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