# Álgebra lineal para Administración y Dirección de Empresas by Emilio Prieto Sáez, Alberto A. Álvarez López

By Emilio Prieto Sáez, Alberto A. Álvarez López

En los capítulos que comprende este texto se exponen los instrumentos matemáticos básicos del Álgebra Lineal, así como una introducción a las sucesiones de números reales. Incluye un tomo con problemas resueltos.

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There now exists a wide literature on the subject of these invariants, and we refer the reader to the Princeton lectures of Racah (24), the work of Weyl (8), and the papers of Stone (2a), Biedenharn (3a), Gef fand and Tsetlin (25), and Louck (26). Topological and geometrical aspects of this problem are discussed in the review of Samelson (27). The method of construction followed by Gel'fand and by Louck is the most economical. , mnn] which were derived in the course of our treatment of the branching theorem.

7. /(m 13 - m 33 + 2)!. Since the Is here are entangled with the 3s in the third row the arm of the hooks extends across the 3s in thefirstrow. ; these nodes are entangled with the 2s in the second row but not with any 3s, so that the arms extend only to the boundary between the Is and the 3s in thefirstrow. REPRESENTATIONS AND TENSOR OPERATORS OF U(n) w33 m22 M23 1 1 . . 22. . 33.. 2 w W\2 1. 1 39 1 3 33.. 3. 3 . 3 FIG. 7 (iii) The arms of the hooks for the next (m23 — m22) Is in the first row extend all the way to the end since these Is are entangled with the 3s below.

3) The operator I2 commutes with all three generators and so, by Schur's Lemma, is a multiple of the unit matrix for an irreducible representation. , that ^ = τ ί ^ / ν ^ ) , where n is an integer. It is useful at this point to re-normalize, setting Jz = Λ/2 H1, so that Jz has the familiar integral or half-integral eigenvalues. 4) Including now a label inasmuch as Ea\J} = 0 and [Ea, E-a] = Ijy/lHx. denoting the highest weight, we see that the state vectors \J, M} of an irreducible representation are uniquely specified.