# Maths - Matrix algebra - 4D arithmatic

The following calculator allows you to calculate 4x4 matrix arithmetic. Enter the values into the matrix into the top two matries and then press "+ - or * " to display the result in the bottom matrix:

=

To add matrices just add the corresponding elements, for 4x4 matrices then,

 a00 + b00 a01 + b01 a02 + b02 a03 + b03 a10 + b10 a11 + b11 a12 + b12 a13 + b13 a20 + b20 a21 + b21 a22 + b22 a23 + b23 a30 + b30 a31 + b31 a32 + b32 a33 + b33
=
 a00 a01 a02 a03 a10 a11 a12 a13 a20 a21 a22 a23 a30 a31 a32 a33
+
 b00 b01 b02 b03 b10 b11 b12 b13 b20 b21 b22 b23 b30 b31 b32 b33

### Matrix Subtraction

To subtract matrices just subtract the corresponding elements, for 4x4 matrices then,

 a00 - b00 a01 - b01 a02 - b02 a03 - b03 a10 - b10 a11 - b11 a12 - b12 a13 - b13 a20 - b20 a21 - b21 a22 - b22 a23 - b23 a30 - b30 a31 - b31 a32 - b32 a33 - b33
=
 a00 a01 a02 a03 a10 a11 a12 a13 a20 a21 a22 a23 a30 a31 a32 a33
-
 b00 b01 b02 b03 b10 b11 b12 b13 b20 b21 b22 b23 b30 b31 b32 b33

### Matrix Multiplication

The multiplication of two 4x4 matrices is:

 ma00*mb00 + ma01*mb10 + ma02*mb20 + ma03*mb30 ma00*mb01 + ma01*mb11 + ma02*mb21 + ma03*mb31 ma00*mb02 + ma01*mb12 + ma02*mb22 + ma03*mb32 ma00*mb03 + ma01*mb13 + ma02*mb23 + ma03*mb33 ma10*mb00 + ma11*mb10 + ma12*mb20 + ma13*mb30 ma10*mb01 + ma11*mb11 + ma12*mb21 + ma13*mb31 ma10*mb02 + ma11*mb12 + ma12*mb22 + ma13*mb32 ma10*mb03 + ma11*mb13 + ma12*mb23 + ma13*mb33 ma20*mb00 + ma21*mb10 + ma22*mb20 + ma23*mb30 ma20*mb01 + ma21*mb11 + ma22*mb21 + ma23*mb31 ma20*mb02 + ma21*mb12 + ma22*mb22 + ma23*mb32 ma20*mb03 + ma21*mb13 + ma22*mb23 + ma23*mb33 ma30*mb00 + ma31*mb10 + ma32*mb20 + ma33*mb30 ma30*mb01 + ma31*mb11 + ma32*mb21 + ma33*mb31 ma30*mb02 + ma31*mb12 + ma32*mb22 + ma33*mb32 ma30*mb03 + ma31*mb13 + ma32*mb23 + ma33*mb33