I found on wikipedia that the following statements are equivalant:(adsbygoogle = window.adsbygoogle || []).push({});

1. Matrix A is left invertible

2. Ax=0 => x=0

I couldn't find the proof so I try to do it myself.

From 1. to 2. is easy. Assume A is left invertible. If Ax=0, then x=Ix=A^{-1}Ax=A^{-1}0 = 0 .

I can't figure out how to do 2=>1. Any help is appreciated.

Things that might prove useful:

- A is injective

- dim(ker(A))=0

- rank(A)=n (if A is an m x n matrix)

- [tex]n\leq m[/tex]

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# Left invertible

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