Cophenetic correlation

Fundamental Matrix in Linear Systems

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

By definition

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

i.e. $\Psi$ is a fundamental matrix of ${\dot {x}}(t)=A(t)x(t)$ if and only if ${\dot {\Psi }}(t)=A(t)\Psi (t)$ and $\Psi$ 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)