2 Attachment(s)

how to multiply out "transpose"?

Hi

I am really confused with the "transpose" related stuff.

Can anyone work me through it?

and the paritial differentiation with respect to it

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why is

$\displaystyle (Y-X\beta)^T(Y-X\beta)=Y^TY-2\beta^TX^TY^T+\beta^TX^TX\beta$

instead of

$\displaystyle (Y-X\beta)^T(Y-X\beta)

=(Y^T-\beta^TX^T)(Y-X\beta)

=Y^TY-Y^TX\beta-\beta^TX^TY+\beta^TX^TX\beta$

and differentiate with respect to beta is

$\displaystyle =-2X^TY+X^TX\beta$