LU Decomposition, why?

There are at least three main advantages with LU decomposition compared with standard Gaussian elimination:

• It is straightforward to compute the determinant of a matrix
• If we have to solve sets of linear equations with the same matrix but with different vectors \( \mathbf{y} \), the number of FLOPS is of the order \( n^3 \).
• The inverse is such an operation

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