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non-negative, then Vᵀ continuous to be a unitary matrix. Hence, to invert U and Vᵀ, we just multiply each one by their transpose, i.e., UᵀU = I and VVᵀ = I. Finding the projection of b — Image by Author If we go further and substitute our best solution x̂ into Ax̂, we will see that most of the