Proof of `Rank and trace of shared frame tensors` (1st statement)
groundedproofs/Lax342547Proofs/TensorIntersections.lean · lax-342547
What this proof establishes
no assumptions
Assuming the claims on the left, the claim on the right holds — checked by the archive's pipeline. Proof code is not displayed here.
Description
An injective linear map identifies every subspace with its image, so left multiplication preserves column rank. Transposition gives the corresponding assertion for right multiplication by the dual frame.