Functions Of Matrices

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A discrete regression method on manifolds and its application to data on SO(n) (2011, methodology): “According to [Higham, 2008, problem 11.1], a Taylor series can be used to deﬁne the principal logarithm of any matrix having no eigenvalue on R − .”
Computing the Karcher mean of symmetric positive definite matrices (2013, methodology): “using the formula M−1 log(K)M = log(M−1KM), valid for any invertible matrix M and any matrix K having real positive eigenvalues (see [12]).”
Technical communique: The Lambert W function and the spectrum of some multidimensional time-delay systems (2007, unknown): “in [12] or [11].”
NLEVP: A Collection of Nonlinear Eigenvalue Problems (2013, unknown): “A ⊗ B denotes the Kronecker product of A and B , namely the block matrix ( a ij B ) [Higham 2008, Sec.”
Scalable Log Determinants for Gaussian Process Kernel Learning (2017, unknown): “where log is the matrix logarithm [29].”
A Riemannian geometry with complete geodesics for the set of positive semidefinite matrices of fixed rank (2013, methodology): “It can be easily computed by means of an eigenvalue decomposition, see Higham (2008).”
A New Scaling and Squaring Algorithm for the Matrix Exponential (2009, unknown): “The tests in [10] and [11] used Sets 1 and 2 together.”