Fundamental matrix (linear differential equation)

Fundamental Matrix in Linear Systems

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

By definition

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

(since each column solves ${\dot {x}}=A(t)x$

A fundamental matrix may refer to

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