Matrix reflection and shear
Description of reflection and shear of matrices with examples
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 twodimensional space.
In the two dimensional space we draw the vector as
Matrices Calculation
Matrices Addition
Matrices Subtraction
Matrices Multiplication
Matrices Inverse Cramer method
Matrices Inverse GaussJordan
Matrices and Simultaneous Equations
Matrices and Determinants
Row Operations of Matrices
Matrices and Geometry, Reflection
Matrices and Geometry, Plane Rotation
The matrix below produces a reflection of the vector across the Xaxis
this results in the formula
A 3dimensional 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 nonzero element into a position outside the diagonal of the unit matrix produces a shear distortion of the position vector.
corresponds to
