I found a research paper that talks about of the orthogonality or the semi orthogonality of the jacobian matrix of a function, that got me wondering about the properties of what if the jacobian matrix is a orthogonal, and what would happen if is only triangular ?
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If $f$ is your function from $\mathbb{R}^n\to \mathbb{R}^n$, then you can write its component functions $f = (f_1,...,f_n)$. If $J(f)$ is triangular then it means $f_i$ is a function which only depends on the first $i$ variables $x_1,...,x_i$. – Nicolas Bourbaki Jan 23 '23 at 17:01