Let \(f : \mathbb{C}^d \to \mathbb{C}^d\) be a birational map and \(\delta(f) := \lim_{n \to \infty} (\deg f^n)^{1/n}\) be its dynamical degree. We note again \(f\) the meromorphic extension to \(\mathbb{C}\mathbb{P}^d\). The authors compute \(\delta(f)\) for a class of maps of the form \(f = L \circ J\), where \(J(x_1,\ldots,x_d) = (x_1^{-1},\ldots,x_d^{-1})\) and \(L\) is an invertible linear map of \(\mathbb{C}^d\). The idea is to look at the action of \(f^*\) on the cohomology group \(H^{1,1}(\mathbb{C}\mathbb{P}^d)\). Indeed, when the identity \((f^*)^n = (f^n)^*\) holds on \(H^{1,1}(\mathbb{C}\mathbb{P}^d)\) (we say that \(f\) is \(1\)-regular), then \(\delta(f)\) is the spectral radius of the linear map \(f^*\). When \(f\) is not \(1\)-regular, one may regularize \(f\), i.e., find a birational equivalence \(h : \mathbb{C}\mathbb{P}^d \to X\) such that \(\tilde f := h \circ f \circ h^{-1}\) is \(1\)-regular on \(X\). J. Diller and C. Favre proved that this operation is always possible in dimension \(2\) [Am. J. Math. 123, 1135–1169 (2001; Zbl 1112.37308)]. The authors consider the problem in higher dimension. They regularize some maps of the form \(L \circ J\), called “elementary”. The interplay between the dynamics of the indeterminacy set and the exceptional set is crucial. They focus on the exceptional varieties that are mapped by some iterate of \(f\) on a point of inderminacy : it gives rise to a so-called “singular” orbit. A map \(f\) is said elementary if it is a local biholomorphism at each point of the singular orbit. The regularization of an elementary map is obtained by blowing up the points of the singular orbits. The spectral radius of the regularized map depends only on two lists \(\mathcal{L}^o , \mathcal{L}^c\) of positive integers determined by the set of singular orbits. Note that most of the maps considered in this article appear naturally in mathematical physics literature.