Question: Example 2.3 shows that changing the pair of bases can change the map that a matrix represents, even though the domain and codomain remain the

Example 2.3 shows that changing the pair of bases can change the map that a matrix represents, even though the domain and codomain remain the same. Could the map ever not change? Is there a matrix H, vector spaces V and W, and associated pairs of bases B1,D1 and B2,D2 (with B1 ≠ B2 or D1 ≠ D2 or both) such that the map represented by H with respect to B1,D1 equals the map represented by H with respect to B2,D2?

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