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The trace of an Square Matrix A is defined by
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(1) |
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(2) |
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(3) |
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(4) |
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(5) |
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(6) |
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(7) |
The trace of a product of square matrices is independent of the order of the multiplication since
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(8) |
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(9) |
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(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
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(11) |
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(12) |
References
Lang, S. Linear Algebra, 3rd ed. New York: Springer-Verlag, pp. 40 and 64, 1987.
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© 1996-9 Eric W. Weisstein