# Why approximate pairwise distances only over lower triangle of distance matrix?

In the context of dimensionality reduction.

Why approximate pairwise distances only over lower triangle of distance matrix?

$$\min_{\{\hat{x_i}\}} I = \sum_{i <j} ({ \hat{ d_{ij} } - d_{ij} })^2$$

(also known as raw stress)

Where $d_{ij}$ are distances of original data points and $\hat{d_{ij}}$ contain new coordinates that would approximate pairwise distances.

(as my notes give)

Is it perhaps that the upper triangle is a duplicate of the lower, since surely $d_{ij}=d_{ji}$ ($i \not= j$)?

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