Cophenetic correlation

Fundamental Matrix in Linear Systems

The fundamental matrix of $\dot{x}(t)=A(t)x(t)$ is the matrix $\mathrm{\Psi }$ such that the n columns are linearly independent solutions of $\dot{x}(t)=A(t)x(t)$.

By definition

$\dot{\mathrm{\Psi }}(t)=A(t)\mathrm{\Psi }(t)$

i.e. $\mathrm{\Psi }$ is a fundamental matrix of $\dot{x}(t)=A(t)x(t)$ if and only if $\dot{\mathrm{\Psi }}(t)=A(t)\mathrm{\Psi }(t)$ and $\mathrm{\Psi }$ is a non-singular matrix for all $t$.

References

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A fundamental matrix may refer to

• fundamental matrix (computer vision)
• fundamental matrix (linear differential equation)
• fundamental matrix (absorbing markov chain)