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Topic: Square of a lower triangular matrix
Replies: 2   Last Post: Apr 14, 2013 6:12 PM

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Kaba

Posts: 289
Registered: 5/23/11
Re: Square of a lower triangular matrix
Posted: Apr 14, 2013 5:36 PM
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15.4.2013 0:05, HardySpicer wrote:
> If I have a lower (say n square) triangular matrix T and I compute
> T^2 is there a proof which says that it too must be a lower triangular
> matrix with diagonal elements the square of the original?


Yes. A generalization: given A, B in R^{n x n} lower-triangular, then AB
is lower-triangular, with diag(AB) = diag(A) diag(B), where diag() sets
all off-diagonal elements zero.

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http://kaba.hilvi.org



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