Identity matrix of size 1:

Identity matrix of size 2:

Identity matrix of size 3:

Identity matrix of size 4:

Identity matrix of size 5:

Cross product of [1] and itself:

Cross product of [1,0, 0,1] and itself:

Cross product of [1,0,0, 0,1,0, 0,0,1] and itself:

Cross product of [2,3, -2,-1] and [4,0, 1,2]:

Cross product of [1,2,3, 1,2,3, 1,2,3] and [0,1,2, -1,-1,-1, 1,1,1]:

Remember that sin(π/4)=√(½)=

Vector [0,1,0] rotated 0:

Vector [0,1,0] rotated π/4:

Vector [0,1,0] rotated π/2:

Vector [0,1,0] rotated π:

Vector [0,1,0] rotated -π:

Vector [0,1,0] rotated 3π/2:

Vector [0,1,0] rotated 2π:

Vector [0,1,0] rotated π/4 and again by π/4:

Vector [0,1,0] rotated π/4 and again by -π/4:

Vector [1,0,0] rotated 0:

Vector [1,0,0] rotated π/4:

Vector [1,0,0] rotated π/2:

Vector [1,0,0] rotated π:

Vector [1,0,0] rotated -π:

Vector [1,0,0] rotated 3π/2:

Vector [1,0,0] rotated 2π:

Vector [1,0,0] rotated π/4 and again by π/4:

Vector [1,0,0] rotated π/4 and again by -π/4:

Vector [1,0,0] rotated 0:

Vector [1,0,0] rotated π/4:

Vector [1,0,0] rotated π/2:

Vector [1,0,0] rotated π:

Vector [1,0,0] rotated -π:

Vector [1,0,0] rotated 3π/2:

Vector [1,0,0] rotated 2π:

Vector [1,0,0] rotated π/4 and again by π/4:

Vector [1,0,0] rotated π/4 and again by -π/4:

Vector [1,1,1] scaled 2× in *x* direction:

Vector [1,1,1] mirrored -2× in *y* direction:

Vector [1,1,1] scaled ½× in *z* direction:

Vector [1,1,1] scaled 1× in each direction:

Vector [1,1,1] mirrored -1× in each direction:

Vector [1,1,1] scaled 0× in each direction:

Vector [1,1,1] scaled 1000× in each direction:

Vector [1,1,1] scaled by 2× then again ½× in each direction:

Vector [1,1,1] scaled by 2× then again 3× in each direction:

Vector [0,0,0] translated by 8 along *x*-axis:

Vector [0,0,0] translated by -8 along *y*-axis:

Vector [0,0,0] translated by 8 along *z*-axis:

Vector [0,0,0] translated by 0:

Vector [0,0,0] translated by 8 along each axis:

Vector [0,0,0] translated by 8 and then again by -8 along each axis:

Vector [0,0,0] translated by 4 and then again by 4 along each axis:

Vector [0,0,0] translated by 8 in *x* and then again by 5 in *y*:

(RR) Vector [1,0,0] rotated π/2 around *z*-axis
(result is ),
then again π/2 around the *x*-axis.

(**RS**) Vector [1,1,1] rotated π/2 around *z*-axis
(result is ),
then scaled 2× along *x* direction.

(SR) Vector [1,1,1] scaled 2× along *x* direction
(result is ),
then rotated π/2 around *z*-axis.

(**ST**) Vector [1,1,1] scaled 2× in each direction
(result is ),
then translated by 1 in *y* direction:

(TS) Vector [1,1,1] translated by 1 in *y* direction
(result is ),
then scaled 2× in each direction:

(TRT) Vector [0,0,0] translated 1 in *y*, then rotated π around *z*,
then translated 1 in *y* again:

(TRTR) Vector [0,1,0] translated 1 in *y*, rotated π/2 around *z*-axis,
translated 1 in *y* again, and finally rotated π/2 around *z* again:

(RTRT) Vector [0,1,0] rotated π/2 around *z*-axis, translated 1 in *y*,
rotated π/2 around *z* again, and finally translated 1 in *y* again:

(RT) Build a transformation matrix that first rotates π/2 around *z* then translates 1 in *y*. Apply to [0,0,0]:

(TT) Build a transformation matrix that first scales 2× in each direction then translates 1 in *y*. Apply to [0,0,0]:

See also Concatenating Transforms for
more information about how to perform local and global transformations.