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• CommentRowNumber1.
• CommentAuthorzskoda
• CommentTimeJan 3rd 2014
• (edited Jan 3rd 2014)

I have created dual basis in the natural generality of projective modules. The corresponding redirects removed from dual vector space entry whose dual basis definition is absorbed in a remark here (without changes to the original).

1. The sentence “In particular, $x_i^*(x_j) = \delta_i^j$ (Kronecker delta)” is incorrect: there may be relations between the $x_j$’s, e.g. $x_2=3x_1$, then apply $x_2^*$ to the two sides we will get $1=3\cdot 0=0$, impossible.

Peng DU

2. Fixed a small typo and added a sentence.

• CommentRowNumber4.
• CommentAuthorTodd_Trimble
• CommentTimeMar 6th 2019

Well, that’s not the only thing wrong in the paragraph mentioned by Deng PU. I’ll have a look later to see what can be salvaged.