Matrix factorization is a crucial technique for calculations, but improper modeling can lead to inefficiencies and errors. The key is to properly understand how to represent and manipulate matrices in code. Earlier discussions emphasized understanding calculations without focusing on the correct modeling of matrices.

In the previous setup, matrices were specified only by columns, creating confusion. Correct matrix modeling requires recognizing them as dynamic entities, not static arrays, applicable across multiple dimensions. For clarity, matrices should be seen as one-dimensional arrays in a multidimensional space.

Consideration of element ordering in arrays directly affects matrix operation implementations. Element arrangement dictates necessary code transitions. Aligning these orders to computation needs is essential. Enhancing code for larger matrices...
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