Manuscript XVI-O1-ST@5 · XVI-O1-ST-v5.tex · proposition · dd45e0d1

Proposition: Complete right-kernel certificate

Exact rank certificates and the repaired affine family · lines 751–762 · proof included or linked

XVI-O1-ST@5#prop:right

If $rank M = r$ , $M Z = 0$ , and $Z \in K^{p \times (p - r)}$ has rank $p - r$ , then $im Z = ker M$ . With a verified particular solution, all solutions are $c_{⋆} + Z t$ .

Proof. The inclusion and dimensions agree.

Nearby in this section

section: Exact rank certificates and the repaired affine family
theorem: Theorem: Rank–minor–left-kernel certificate
section: Exact rank certificates and the repaired affine family
section: Exact rank certificates and the repaired affine family
theorem: Theorem: Permanent affine false-positive witness
section: Exact rank certificates and the repaired affine family