Buscar

Loading [MathJax]/jax/output/HTML-CSS/jax.js

9.2: Ortogonalización Gram-Schmidt
https://espanol.libretexts.org/Matematicas/Algebra_lineal/Libro%3A_An%C3%A1lisis_Matriz_(Cox)/09%3A_El_problema_del_valor_propio_sim%C3%A9trico/9.02%3A_Ortogonalizaci%C3%B3n_Gram-Schmidt
Es decir, $y_{2} = x_{2}-q_{1}(q_{1}^{T}q_{1})^{-1}q_{1}^{T}x_{2} = x_{2}-q_{1}q_{1}^{T}x_{2} \nonumber$ Set $q_{2} = \frac{y_{2}}{||y_{2}||}$ y $Q_{2} = \{q_{1}, q_{2}\}$ \[y_{3} = x_{3}-Q_{2}(Q_{...Es decir, $y_{2} = x_{2}-q_{1}(q_{1}^{T}q_{1})^{-1}q_{1}^{T}x_{2} = x_{2}-q_{1}q_{1}^{T}x_{2} \nonumber$ Set $q_{2} = \frac{y_{2}}{||y_{2}||}$ y $Q_{2} = \{q_{1}, q_{2}\}$ $y_{3} = x_{3}-Q_{2}(Q_{2}^{T}Q_{2})^{-1}Q_{2}^{T} x_{3} = x_{3}-q_{1}q_{1}^{T}x_{3} \nonumber$ Establecer $q_{3} = \frac{y_{3}}{||y_{3}||}$ y $Q_{3} = \{q_{1}, q_{2}, q_{3}\}$ . $y_{2} = x_{2}-q_{1}q_{1}^{T}x_{2} = \begin{pmatrix} {0}&{1}&{0} \end{pmatrix}^T$ y así, $q_{2} = y_{2}$

Search