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Fermat
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#1
Report Thread starter 16 years ago
#1
(Matrices)

Suppose x=[x1,...xm], and y=[y1,...yn] are column vectors (m x 1 and n x 1 respectively), and that A is an n x m matrix. Show that :

(i) yTAx = (yTAx)T
(ii) (y - Ax)T(y - Ax) = yTy - 2yTAx + xTATAx

where the capital T means the transpose of the vector or matrix just to the left of it.
i.e. yT means the transpose of y.
(y - Ax)T means the transpose of (y - Ax).
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Jonny W
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Report 16 years ago
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y^T is 1 by n,
A is n by m,
x is n by 1.

So

y^T A x

is 1 by 1. Taking the transpose of a 1 by 1 matrix is quite easy!
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Fermat
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#3
Report Thread starter 16 years ago
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(Original post by Jonny W)
y^T is 1 by n,
A is n by m,
x is n by 1.

So

y^T A x

is 1 by 1. Taking the transpose of a 1 by 1 matrix is quite easy!
That's right. These were listed as difficult in my Unit on matrix algebra! The 2nd part uses a similar approach.
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