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 a Lie group and the logarithm is the corresponding element of the Lie algebra.
Read more about Logarithm Of A Matrix: Definition, Example: Logarithm of Rotations in The Plane, Existence, Properties, Further Example: Logarithm of Rotations in 3D Space, Calculating The Logarithm of A Diagonalizable Matrix, The Logarithm of A Non-diagonalizable Matrix, A Functional Analysis Perspective, A Lie Group Theory Perspective, Constraints in 2 × 2 Case
Famous quotes containing the word matrix:
“As all historians know, the past is a great darkness, and filled with echoes. Voices may reach us from it; but what they say to us is imbued with the obscurity of the matrix out of which they come; and try as we may, we cannot always decipher them precisely in the clearer light of our day.”
—Margaret Atwood (b. 1939)