Switching Rows and Columns w/ Tricky Dot Products (Follow-Up to 2011 Putnam A4)

[@mohithraju2629]

slightly pedantry here, 1. we have proved if AA^t = I^r then (A^r)(A^r)^t = I and thus (A^r)^t(A^r) = I . Now we have to conclude that columns of have the 'property'. We cannot just use what we have proved before because the right hand side has I instead of I^r. A similar proof obviously works to give A^tA = I^r [this was not immediately obvious to me until I wrote it down on paper] 2. To show the iff statement we also have to show that all even matrices DO NOT have the 'column property' mentioned in video. This is easily shown by the same contradiction used to show that the rows do NOT have the 'property'. Great video! thank you

[@LetsSolveMathProblems]

You are absolutely right, and I agree that the first implicit lemma you mentioned (at 9:20 in the video) is not obvious at first glance. I completely forgot to address this issue in this video. Thank you for notifying me!

[@azerbenmed8597]

Finally you're back Let's solve math Problems. You're the best math youtuber.

[@arshsverma]

I just found you a few days ago and am going through all your weekly challenges and other video, great work, keep posting

[@uttkarshkohli-mathchannel8284]

good to have you back

[@qschroed]

First time I actually managed to solve one of the problems!

[@yassinezaoui4555]

Great Job ^^