- #1

- 61

- 5

[tex]s^T L s L s = L s s^T L s [/tex]

by noticing that [tex] s^TLs[/tex] is a scalar.

However,

[tex] s^T L s L \neq L s s^T L [/tex].

Is there some mathematical explanation behind this? Thank you.

elgen

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- Thread starter elgen
- Start date

- #1

- 61

- 5

[tex]s^T L s L s = L s s^T L s [/tex]

by noticing that [tex] s^TLs[/tex] is a scalar.

However,

[tex] s^T L s L \neq L s s^T L [/tex].

Is there some mathematical explanation behind this? Thank you.

elgen

- #2

Staff Emeritus

Science Advisor

Gold Member

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[tex]\begin{pmatrix}0 & 0 & 0\\ 0 & 1 & 0\\ 0 & 0 & 1\end{pmatrix}\begin{pmatrix}1 \\ 0\\ 0\end{pmatrix}=0[/tex]

Here A projects onto the 23 plane, and x is in the 1 direction.

- #3

- 61

- 5

What has surprised me is that, let [tex]\alpha=s^TL s [/tex], the equality is really

[tex]\alpha Ls = L s \alpha [/tex].

Since

[tex]s^T L s Ls = L s s^T L s[/tex]

we have

[tex](s^T Ls L - L s s^T L)s = 0 [/tex]

This does not imply that [tex] s^T L s L = L s s^T L[/tex].

- #4

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- #5

- 61

- 5

Thank you for the discussion.

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