How do I prove that if A is onto then its transpose is one-to-one?

Asked May 02 '19 at 19:15

Active May 02 '19 at 19:15

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I want to prove that if A is onto then its transpose is one-to one. Here $A\in R^{nxm}$.

asked May 02 '19 at 19:15

rose

2

Row rank equals column rank. – Angina Seng May 02 '19 at 19:19
The trouble with "coordinate-based" approach to linear algebra is that it doesn't disclose the geometric content of the subject. As is indicated in the duplicate, you will find it much more intuitive and instructive to work with the dual of a linear transformation, rather than with the transpose of a matrix. – avs May 02 '19 at 21:11

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