Logarithm of a matrix: Difference between revisions

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Thus, the matrix ''A'' has infinitely many logarithms. This corresponds to the fact that the rotation angle is only determined up to multiples of 2''π''.

In the language of Lie theory, the rotation matrices ''A'' are elements of the Lie group [[circle group|SO(2)]]. The corresponding logarithms ''B'' are elements of the Lie algebra soSO(2), which consists of all [[skew-symmetric matrix|skew-symmetric matrices]]. The matrix

:<math>

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</math>

is a generator of the [[Lie algebra]] soSO(2).

==Existence==