Let A and B be matrices having more rows than columns. It's obvious that if [A,B] has full column rank, then A and B have full column rank. But what if [A,B]^T has full column rank. Then it doesn't imply that A or B have full column rank, right? (Also the converse direction doesn't work, right?)

Rohan Mcpherson 2022-10-02 Answered
Let A and B be matrices having more rows than columns. It's obvious that if [A,B] has full column rank, then A and B have full column rank.
But what if [ A , B ] T has full column rank. Then it doesn't imply that A or B have full column rank, right?
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Answers (1)

Carson Mueller
Answered 2022-10-03 Author has 7 answers
Let A = [ 1 0 0 0 0 0 ] and B = [ 0 0 1 0 0 1 ] . Then [ A , B ] has full column rank but A does not.
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