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I have a matrix $K_{3x3}$ that I would like to convert into a matrix of the form: $$ L' = \begin{bmatrix} a & 0 & 0 \\ b & 1 & 0 \\ c & 0 & 1 \\ \end{bmatrix} $$ by multiplying it with a series of Givens rotation matrices: $$ L'KLG_1G_2...G_n $$ Is this at all possible? If so what sequence of Givens rotations annihilates the correct elements?

Is there some other way I can uniquely decompose: $$ K = L'R $$ where R is an orthogonal matrix?

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  • $\begingroup$ Then $\det(K)=\pm \det(L')=\pm a$, but this might not be true. $\endgroup$
    – Dietrich Burde
    Commented 8 hours ago
  • $\begingroup$ If $K=0_{3\times 3}$, you can't. $\endgroup$
    – Gonçalo
    Commented 7 hours ago

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