I am having problems in proving the following equation: Let $A=I-J$, where $I$ is an identity matrix, and $J$ is antisymmetric, and let $M$ be symmetric and positive definite. Then $$A\left[\int_0^\infty e^{-As}Me^{-A^Ts}ds+\left(\int_0^\infty e^{-As}Me^{-A^Ts}ds\right)^T\right]=2M.$$ Could anyone help? Thanks for any comment!
2026-04-29 07:36:27.1777448187
Equations regarding exponential of matrices
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