Helper

kernel_membership

File dumas2017dual/lib/rouche_capelli.v
Section RoucheCapelliTheorems
Type Lemma
Proof Lines 4

Signature

Lemma kernel_membership m n p (A : 'M[R]_(m, n)) (X : 'M[R]_(n, p)) : A *m X = 0 -> (X^T <= kermx A^T)%MS.

Description

Solutions to AX = 0 lie in the kernel: if AX = 0, then X^T ≤ ker(A^T). Transposes relate left/right multiplication to kernel membership.

Uses (0)

This lemma does not use any other lemmas from the stats.

Used By (0)

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