A Note on Parameter Differentiation of Matrix Exponentials, with Applications to Continuous-time Modeling (short Running Title: Parameter Differentiation of Matrix Exponentials)
نویسنده
چکیده
We have derived a new analytic formula for evaluating the derivatives of a matrix exponential. In contrast to some existing methods, eigenvalues and eigenvectors do not appear explicitly in the formulae, although we show that a necessary and sufficient condition for the validity of the formulae is that the matrix has distinct eigenvalues. The new formula expresses the derivatives of a matrix exponential in terms of minors, polynomials, exponential of the matrix as well as matrix inver-
منابع مشابه
A note on parameter differentiation of matrix exponentials, with applications to continuous-time modelling
We propose a new analytic formula for evaluating the derivatives of a matrix exponential. In contrast to the diagonalization method, eigenvalues and eigenvectors do not appear explicitly in the derivation, although we show that a necessary and sufficient condition for the validity of the formula is that the matrix has distinct eigenvalues. The new formula expresses the derivatives of a matrix e...
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