Linear Algebra Proof

  • Thread starter vg19
  • Start date
  • #1
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Hi,

There is an example of this question in the book but I cannot understand the part where it says 2AT = 2[2AT]T. Everything else I understand. (T means Transpose)

Suppose a square matrix A satisfies A = 2AT. Show that necessarily A=0.

A = 2AT = 2[2AT]T = 2[2(AT)T] = 4A

3A = 0
A=1/3(3A) = 1/3(0) = (0)


Thanks!
 

Answers and Replies

  • #2
128
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They are just using the assumption [itex]A = 2A^T[/itex] in that step.
 
  • #3
67
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I think I get it. So basically are they doing that step to get rid of the Transpose so A will be alone, and then can be isolated?

Thanks
 
  • #4
128
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vg19 said:
I think I get it. So basically are they doing that step to get rid of the Transpose so A will be alone, and then can be isolated?

Thanks
Yes, you could say that. :smile:
 

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