Unlike the scalar logarithm, there are no naturally-defined bases for the matrix logarithm; therefore, the matrix logarithm is always taken to be the natural logarithm. In general, there may be an infinite number of matrices satisfying ; these are known as the logarithms of .
As for the scalar natural logarithm, the matrix logarithm can be defined as a power series when is a square matrix and , where is the Frobenius matrix norm. The logarithm this formula produces is known as the principal logarithm of .
There are other, more general methods of calculating the matrix logarithm. For example, see \htmladdnormallinkAn Explicit Formula for the Matrix Logarithmhttp://arxiv.org/abs/math/0410556.
|Date of creation||2013-03-22 15:31:22|
|Last modified on||2013-03-22 15:31:22|
|Owner||Andrea Ambrosio (7332)|
|Last modified by||Andrea Ambrosio (7332)|
|Author||Andrea Ambrosio (7332)|