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March 15th, 2019, 02:50 PM   #1
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If (ui +ei) is LD, prove: sum{|ui|^2} >= 1

Let u1, u2, ..., un be vectors in R^n and e1, e2, ..., en be the canonical basis.

If (ui + ei) is a LD set, the exercise is to prove the inequality:
sum{|ui|^2} >=1

I am trying to suppose, by contradiction, that the sum is less than 1, and then get that the vectors (ui+ei) are LI. I know this exercise is introductory to Linear Algebra, so it doesn't require deep theorems like "Frobenius norm" or matrices knowledge.
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March 16th, 2019, 02:46 PM   #2
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What is LD?
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March 16th, 2019, 05:03 PM   #3
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LD presumably means linearly dependent.
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