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Let $a = [a_1,a_2,\dots,a_n]^T$, $b = [b_1, b_2, \dots, b_n]^T$.

and $C = \begin{bmatrix}c_1^Tc_1 & c_1^Tc_2 & \dots & c_1^Tc_n\\c_2^Tc_1 & c_2^Tc_2 & \dots & c_2^Tc_n\\ \vdots & \vdots & \ddots & \vdots\\c_n^Tc_1 & c_n^Tc_2 & \dots & c_n^Tc_n\end{bmatrix}$

Where ($c_i$) is a list of vectors of the same size.

In order to get $a_i = b_i - \sum_{j = 1}^na_jc_j^Tc_i$

Should it be $a = b - C^Ta$ ? In the book which I am reading, they write $a = b - Ca$.

Please just give me a confirmation, am I correct?

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  • $\begingroup$ Where do $c_i$ belong? What do you mean by $c_i^T$? $\endgroup$
    – Kal S.
    Dec 30, 2013 at 2:59
  • $\begingroup$ @user117757 $c_i$ is a list of vectors of the same size, I'll add this to the main post, thank you for reminding me. $\endgroup$
    – Learner
    Dec 30, 2013 at 3:00
  • $\begingroup$ No problem. It's right. $\endgroup$
    – Shuchang
    Dec 30, 2013 at 3:01
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    $\begingroup$ It's correct. Notice only that $C^T=C$ $\endgroup$
    – Kal S.
    Dec 30, 2013 at 3:03
  • $\begingroup$ Oh I see! Thanks! $\endgroup$
    – Learner
    Dec 30, 2013 at 3:06

1 Answer 1

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C is $n\times n$ matrix and $C^T=C$ so $Ca=C^Ta$.

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