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- Are linear automorphisms nothing but the identity mapping?

Hi Physics Forums,

Quick question! Are every automorphism on a vectors space ## V ## over some field ## \mathbb{F} ## nothing but the identity mapping in disguise?

The reason for asking is; automorphisms are (from my point of view) basically a change of basis, and vectors are invariant under change of basis (their coordinates do indeed change)... So automorphisms are taking every vector to itself?

Thnx

Quick question! Are every automorphism on a vectors space ## V ## over some field ## \mathbb{F} ## nothing but the identity mapping in disguise?

The reason for asking is; automorphisms are (from my point of view) basically a change of basis, and vectors are invariant under change of basis (their coordinates do indeed change)... So automorphisms are taking every vector to itself?

Thnx