My book says that, given a 4x4 rank-3 matrix Q (also positive-definite) and its spectral decomposition (eg, eigen decomposition),(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

Q = V D V^{-1}

[/tex]

it is easy to factor Q as

[tex]

Q = H J H ^\mathsf{T}

[/tex]

where

[tex]

J = \left[

\begin{array}{cccc}

1 & 0 & 0 & 0\\

0 & 1 & 0 & 0\\

0 & 0 & 1 & 0 \\

0 & 0 & 0 & 0

\end{array}

\right]

[/tex]

Apparently it's so trivial that they didn't waste the space to say how, but I'm not seeing how to do it...

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# Easy decomposition question

Can you offer guidance or do you also need help?

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