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Hi,

I have a matrix : $W=I+U^TV$

• $dim(W)=(D,D)$
• $dim(U)=dim(V)=(N,D)$ with $N < < D$

I need it to be orthogonal ie $W^TW=I$

which gives me : $V^TU+U^T+V^TUU^TV=0$ V^TU+U^TV+V^TUU^TV=0$From that point, i don't know where to go. Have anyone got some ideas about that issue ? Cheers Guillaume 1 # decomposition of an orthogonal matrix Hi, I have a matrix :$W=I+U^TV$•$dim(W)=(D,D)$•$dim(U)=dim(V)=(N,D)$with$N < < D$I need it to be orthogonal ie$W^TW=I$which gives me :$V^TU+U^T+V^TUU^TV=0\$

From that point, i don't know where to go. Have anyone got some ideas about that issue ?

Cheers

Guillaume