Helper

card_lker_mxof

File dumas2017dual/lib/rouche_capelli.v

Section card_lker

Type Lemma

Proof Lines 7

Signature

Lemma card_lker_mxof : #|(lker f)| = #|[set x : 'rV[K]_(\dim {:aT}) | x *m (mxof e e' f) == 0]|.

Description

Kernel cardinality via matrix representation: |ker(f)| = |{x | x·M = 0}| where M is the matrix of f w.r.t. bases e, e'. Bridges abstract linear maps to concrete matrix equations for counting.

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