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singular value decomposition
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Computational Inputs:

» matrix:

Input

singular value decomposition | (1 | 0 | -1 -2 | 1 | 4)

Result

M = U.Σ.V^† where M = (1 | 0 | -1 -2 | 1 | 4) U = ((19 - sqrt(505))/(12 sqrt(1 + 1/144 (19 - sqrt(505))^2)) | (19 + sqrt(505))/(12 sqrt(1 + 1/144 (19 + sqrt(505))^2)) 1/sqrt(1 + 1/144 (19 - sqrt(505))^2) | 1/sqrt(1 + 1/144 (19 + sqrt(505))^2)) Σ = (sqrt(1/2 (23 + sqrt(505))) | 0 | 0 0 | sqrt(1/2 (23 - sqrt(505))) | 0) V = ((1/12 (19 - sqrt(505)) - 2)/sqrt(1 + (1/12 (19 - sqrt(505)) - 2)^2 + (4 + 1/12 (sqrt(505) - 19))^2) | (1/12 (19 + sqrt(505)) - 2)/sqrt(1 + (4 + 1/12 (-19 - sqrt(505)))^2 + (1/12 (19 + sqrt(505)) - 2)^2) | 1/sqrt(6) 1/sqrt(1 + (1/12 (19 - sqrt(505)) - 2)^2 + (4 + 1/12 (sqrt(505) - 19))^2) | 1/sqrt(1 + (4 + 1/12 (-19 - sqrt(505)))^2 + (1/12 (19 + sqrt(505)) - 2)^2) | -sqrt(2/3) (4 + 1/12 (sqrt(505) - 19))/sqrt(1 + (1/12 (19 - sqrt(505)) - 2)^2 + (4 + 1/12 (sqrt(505) - 19))^2) | (4 + 1/12 (-19 - sqrt(505)))/sqrt(1 + (4 + 1/12 (-19 - sqrt(505)))^2 + (1/12 (19 + sqrt(505)) - 2)^2) | 1/sqrt(6))
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