Calculate singular value decomposition
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I need to find the reduced singular value decomposition of this matrix. $$begin{pmatrix} -2 & -1 & 2 \ 2 & 1 & -2 \ end{pmatrix} $$ I formed $$ A^TA= begin{pmatrix} 8 & 4 & -8 \ 4 & 2 & -4 \ -8 & -4 & 8 \ end{pmatrix} $$ Found the eigenvalue 18 and eigenvector $$begin{pmatrix} -1 \ -1/2 \ 1 end{pmatrix}$$ $$ u_1=begin{pmatrix} frac{3sqrt2}{4} \ frac{-3sqrt2}{4} end{pmatrix} $$ So $$ A=begin{pmatrix} frac{3sqrt2}{4} \ frac{-3sqrt2}{4} end{pmatrix}begin{pmatrix}3sqrt2end{pmatrix}begin{pmatrix} -1 & -1/2 & 1 end{pmatrix} $$ But this is clearly not correct
linear-algebra matrix-decomposition
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