linear algebra matrix transformations

reflection about the x-axis

reflection about the y-axis

reflection about the line y=x

reflection about the origin

orthogonal projection onto the x-axis

orthogonal projection onto the y-axis

rotation about the origin through a positive angle θ

expansion in the x-direction with factor k

(k > 1)

expansion in the y-direction with factor k

(k > 1)

compression in the x-direction with factor k

(0 < k < 1)

compression in the y-direction with factor k

(0 < k < 1)

shear in the positive x-direction by a factor k

(k > 0)

shear in the negative x-direction by a factor k

(k < 0)

shear in the positive y-direction by a factor k

(k > 0)

shear in the negative y-direction by a factor k

(k < 0)