Chemistry Reference
In-Depth Information
Comparing this with Equation (A5.24), you will see that, as stated earlier, the inverse is
simply the transpose of the original matrix. This is also a general property of matrices
which represent symmetry operations, and it makes finding these inverses much easier
than following this standard formula route. You should also be able to see that the inverse
matrix is the same as the matrix we defined for
C
4
3
in the main text, i.e. the inverse matrix
correctly gives the inverse symmetry operation.
As a check of the calculation, we form the product of the matrix and its inverse:
⎛
⎞
⎛
⎞
⎛
⎞
010
0
10
100
001
−
100
010
001
⎝
⎠
⎝
⎠
=
⎝
⎠
=
(
C
4
1
)
−
1
C
4
1
=
−
100
001
E
(A5.28)
so the inverse multiplied into the matrix gives the identity matrix as required.
Further Reading
Steiner E (1996)
The Chemistry Maths Book
. Oxford Science Publications (ISBN 0 19 855913 5).
Lambourne R, Tinker M (2000)
Basic Mathematics for the Physical Sciences
, Wiley (ISBN 0 471
82507 4).
Lambourne R, Tinker M (2000)
Further Mathematics for the Physical Sciences
, Wiley (ISBN 0 471
86723 3).
