Reducible Matrix

A Square $n\times n$ matrix ${\hbox{\sf A}}=a_{ij}$ is called reducible if the indices 1, 2, ..., $n$ can be divided into two disjoint nonempty sets $i_1$, $i_2$, ..., $i_\mu$ and $j_1$, $j_2$, ..., $j_\nu$ (with $\mu+\nu=n$) such that

$$a_{i_\alpha j_\beta}=0$$

for $\alpha=1$, 2, ..., $\mu$ and $\beta=1$, 2, ..., $\nu$. A Square Matrix which is not reducible is said to be Irreducible.

See also Square Matrix

References

Gradshteyn, I. S. and Ryzhik, I. M. Tables of Integrals, Series, and Products, 5th ed. San Diego, CA: Academic Press, p. 1103, 1979.