Page 143 - Textos de Matemática Vol. 39

Case 3.

MATRIX PENCILS 133
If q = 1, the proof is complete. If q ≥ 2, then, according to the induction assumption, G is strictly equivalent to a pencil containing a zero subpencil of size p × (q − 1). It is easy to complete the proof.
Case 4. Suppose that Ax + B has a row minimal index. Analogous to
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