We define a notion of depth for an inclusion of multimatrix algebras $B
\subseteq A$ based on a comparison of powers of the induction-restriction table
$M$ (and its transpose matrix). The depth of the semisimple subalgebra $B$ in
the semisimple algebra $A$ is the least positive integer $n \geq 2$ for which
$M^{n+1} \leq qM^{n-1}$ for some $q \in \Z_+$. We prove that a depth two
subalgebra is a normal subalgebra, and conversely. As a corollary, a depth $n$
subalgebra is a normal subalgebra of its $(n-2)$'nd iterated endomorphism
algebra in a tower above $B \subseteq A$.