  We describe derivations and automorphisms of infinite tensor products of
matrix algebras. Using this description we show that for a
countable--dimensional locally matrix algebra $A$ over a field $\mathbb{F}$ the
dimension of the Lie algebra of outer derivations of $A$ and the order of the
group of outer automorphisms of $A$ are both equal to
$|\mathbb{F}|^{\aleph_0},$ where $|\mathbb{F}|$ is the cardinality of the field
$\mathbb{F}.$
