Computation of the Golden Matrix Exponential Functions of Special Matrices

Computation of the matrix exponential functions is important in solving various scientific and engineering problems due to their active role in solving differential equations. Accurate and effective computation of these functions determines the success of mathematical analysis and practical applications. Therefore, studying and understanding matrix exponential functions is the key to developing mathematical and engineering sciences. In the present paper, we aim to compute the values of the $1$st and $2$nd type Golden matrix exponential functions for some special matrices. We present the similarities and differences with the value of the well-known matrix exponential function for the same special matrices.