The trace of an Square Matrix A is defined by
(1) |
(2) | |||
(3) | |||
(4) |
(5) |
(6) |
(7) |
The trace of a product of square matrices is independent of the order of the multiplication since
(8) |
(9) |
(10) |
The value of the trace can be found using the fact that the matrix can always be transformed to a coordinate system where the
z-Axis lies along the axis of rotation. In the new coordinate system, the Matrix is
(11) |
(12) |
References
Lang, S. Linear Algebra, 3rd ed. New York: Springer-Verlag, pp. 40 and 64, 1987.
© 1996-9 Eric W. Weisstein