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In mathematics, the matrix exponential is a matrix function on square matrices analogous to the ordinary exponential function. Abstractly, the matrix exponential gives the connection between a matrix Lie algebra and the corresponding Lie group. Let be an real or complex matrix. The exponential of , denoted by or , is the matrix given by the power series : The above series always converges, so the exponential of is well-defined. If is a 1×1 matrix the matrix exponential of is a 1×1 matrix whose single element is the ordinary exponential of the single element of . ==Properties== Let and be complex matrices and let and be arbitrary complex numbers. We denote the identity matrix by and the zero matrix by 0. The matrix exponential satisfies the following properties: * * * * If then * If is invertible then * , where denotes the transpose of . It follows that if is symmetric then is also symmetric, and that if is skew-symmetric then is orthogonal. * , where denotes the conjugate transpose of . It follows that if is Hermitian then is also Hermitian, and that if is skew-Hermitian then is unitary. * A Laplace transform of matrix exponentials amounts to the resolvent, . 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Matrix exponential」の詳細全文を読む スポンサード リンク
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