Answer by Yiorgos S. Smyrlis for Space of solutions of $n$-th order ODE via...
The Jordan form looks, in a block form, like$$J=\mathrm{diag}(J_0,J_1,\ldots,J_k),$$where $J_0,J_1,\ldots,J_k$ are submatrices. In particular, $J_0$ is...
View ArticleSpace of solutions of $n$-th order ODE via space of solutions of first order ODE
Consider the $n$-th order ODE $$0=a_0x+\dots+a_{n-1}x^{(n-1)}+a_nx^{(n)}\quad (\star_1)$$ Any solution $u$ of $\dot x = Ax$ $(\star_2)$ with $$A = \begin{bmatrix} 0 & 1 & 0 & \dots &...
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