Identity Matrix
Inverse Matrix
Product of a Matrix and a Vector
Rotations
Rotation-Dilations
Orthogonal Projections
Reflections
Determinant and Inverse of a 2x2 Matrix
Matrix ProductsHow to Examples Exercise
How to:
Causing a vector to rotate in 2-dimensional space can be accomplished by the use of trigonometry functions. The matrix of a counter-clockwise rotation through an angle 'a' is represented by:
A = [cos(a) -sin(a); sin(a) cos(a)]
Remember, it is important that 'a' is represented in radians and not degrees.
Examples:
Let's take the vector x = [2; 0] and rotate it by 270 degrees. In radians this is 3*pi/2:
a = 3*pi/2
A = [cos(a) -sin(a); sin(a) cos(a)]
y = A*x
This gives us the result y = [0; -2]. Our original vector 'x' was stretched out a length of two in the positive-x direction and our rotated vector 'y' is also stretched a length of two, but this time rotated 270 degrees in the negative-y direction.
Exercise: