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Logarithm of a matrix - Wikipedia

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In mathematics, a logarithm of a matrix is another matrix such that the matrix exponential of the latter matrix equals the original matrix. It is thus a generalization of the scalar logarithm and in some sense an inverse function of the matrix exponential. Not all matrices have a logarithm and those matrices that do have a logarithm may have more than one logarithm. The study of logarithms of matrices leads to Lie theory since when a matrix has a logarithm then it is in an element of a Lie group and the logarithm is the corresponding element of the vector space of the Lie algebra. The exponential of a matrix A is defined by Given a matrix B, another matrix A is said to be a matrix logarithm of B if eA = B. Because the exponential function is not bijective for complex numbers (e.g. 𝑒 𝜋 𝑖 = 𝑒 3 𝜋 𝑖 = − 1 ), numbers can have multiple complex logarithms, and as a consequence of this, some matrices may have more than one logarithm, as explained below. If the matrix logarithm of 𝐵

Logarithm of a matrix - Wikipedia Jump to content From Wikipedia, the free encyclopedia Mathematical operation on invertible matrices In mathematics , a logarithm of a matrix is another matrix such that the matrix exponential of the latter matrix equals the original matrix. It is thus a generalization of the scalar logarithm and in some sense an inverse function of the matrix exponential . Not all matrices have a logarithm and those matrices that do have a logarithm may have more than one logarithm. The study of logarithms of matrices leads to Lie theory since when a matrix has a logarithm the

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