Oops

1 files changed, 26 insertions, 26 deletions

diff --git a/anm/n1.lyx b/anm/n1.lyx
index b001a5b..c16347d 100644
--- a/anm/n1.lyx
+++ b/anm/n1.lyx
@@ -147,7 +147,7 @@ Llamamos
 \end_inset
 
 , o 
-\begin_inset Formula ${\cal M}_{n}(A):={\cal M}_{nn}(A)$
+\begin_inset Formula ${\cal M}_{n}(A)\coloneqq {\cal M}_{nn}(A)$
 \end_inset
 
 , pudiendo omitir 
@@ -184,7 +184,7 @@ Dadas
 \end_inset
 
 , llamamos 
-\begin_inset Formula $X+Y:=(X_{ij}+Y_{ij})_{1\leq i\leq m}^{1\leq j\leq n}$
+\begin_inset Formula $X+Y\coloneqq (X_{ij}+Y_{ij})_{1\leq i\leq m}^{1\leq j\leq n}$
 \end_inset
 
 , y dadas 
@@ -196,7 +196,7 @@ Dadas
 \end_inset
 
 , llamamos 
-\begin_inset Formula $XY:=(\sum_{k=1}^{n}X_{ik}Y_{kj})_{1\leq i\leq m}^{1\leq j\leq p}$
+\begin_inset Formula $XY\coloneqq (\sum_{k=1}^{n}X_{ik}Y_{kj})_{1\leq i\leq m}^{1\leq j\leq p}$
 \end_inset
 
 .
@@ -238,7 +238,7 @@ matriz adjunta
 \end_inset
 
  a 
-\begin_inset Formula $M^{*}:=(\overline{M_{ji}})_{ij}\in{\cal M}_{n\times m}(\mathbb{C})$
+\begin_inset Formula $M^{*}\coloneqq (\overline{M_{ji}})_{ij}\in{\cal M}_{n\times m}(\mathbb{C})$
 \end_inset
 
  y 
@@ -250,7 +250,7 @@ matriz traspuesta
 \end_inset
 
  a 
-\begin_inset Formula $M^{t}:=(M_{ji})_{ij}\in{\cal M}_{n\times m}(\mathbb{C})$
+\begin_inset Formula $M^{t}\coloneqq (M_{ji})_{ij}\in{\cal M}_{n\times m}(\mathbb{C})$
 \end_inset
 
 , que coincide con la adjunta cuando los coeficientes son reales, y se tiene
@@ -347,7 +347,7 @@ vector propio
 polinomio característico
 \series default
 , 
-\begin_inset Formula $p_{A}(\lambda):=\det(A-\lambda I)$
+\begin_inset Formula $p_{A}(\lambda)\coloneqq \det(A-\lambda I)$
 \end_inset
 
 .
@@ -364,7 +364,7 @@ espectro
 \end_inset
 
  es 
-\begin_inset Formula $\sigma(A):=\{\lambda_{1},\dots,\lambda_{n}\}$
+\begin_inset Formula $\sigma(A)\coloneqq \{\lambda_{1},\dots,\lambda_{n}\}$
 \end_inset
 
  y su 
@@ -372,7 +372,7 @@ espectro
 radio espectral
 \series default
  es 
-\begin_inset Formula $\rho(A):=\max\{|\lambda_{1}|,\dots,|\lambda_{n}|\}$
+\begin_inset Formula $\rho(A)\coloneqq \max\{|\lambda_{1}|,\dots,|\lambda_{n}|\}$
 \end_inset
 
 .
@@ -476,7 +476,7 @@ matriz de coeficientes
 \end_inset
 
  
-\begin_inset Formula $A:=(a_{ij})_{ij}$
+\begin_inset Formula $A\coloneqq (a_{ij})_{ij}$
 \end_inset
 
 , 
@@ -484,7 +484,7 @@ matriz de coeficientes
 columna de términos independientes
 \series default
  a la matriz columna 
-\begin_inset Formula $b:=(b_{i})_{ij}$
+\begin_inset Formula $b\coloneqq (b_{i})_{ij}$
 \end_inset
 
  y 
@@ -852,7 +852,7 @@ Lo probamos primero para
 \end_inset
 
  y 
-\begin_inset Formula $W:=\text{span}(p_{2},\dots,p_{n})$
+\begin_inset Formula $W\coloneqq \text{span}(p_{2},\dots,p_{n})$
 \end_inset
 
 , existen 
@@ -987,7 +987,7 @@ Existe
 \end_inset
 
  unitaria tal que 
-\begin_inset Formula $T:=U^{-1}AU=U^{*}AU$
+\begin_inset Formula $T\coloneqq U^{-1}AU=U^{*}AU$
 \end_inset
 
  es triangular superior, pero 
@@ -1187,7 +1187,7 @@ Para
 \end_inset
 
 , y haciendo 
-\begin_inset Formula $u_{j}:=\frac{f_{j}}{\mu_{j}}$
+\begin_inset Formula $u_{j}\coloneqq \frac{f_{j}}{\mu_{j}}$
 \end_inset
 
  para 
@@ -1330,7 +1330,7 @@ Sean
 \end_inset
 
 ), 
-\begin_inset Formula $E_{k}:=\text{span}\{p_{1},\dots,p_{k}\}$
+\begin_inset Formula $E_{k}\coloneqq \text{span}\{p_{1},\dots,p_{k}\}$
 \end_inset
 
  para cada 
@@ -1375,7 +1375,7 @@ Sean
 \end_inset
 
  unitaria tal que 
-\begin_inset Formula $D:=U^{*}AU=\text{diag}(\lambda_{1},\dots,\lambda_{n})$
+\begin_inset Formula $D\coloneqq U^{*}AU=\text{diag}(\lambda_{1},\dots,\lambda_{n})$
 \end_inset
 
 , 
@@ -1519,7 +1519,7 @@ Queremos ver que
 
 .
  Si 
-\begin_inset Formula $E_{k-1}^{\bot}:=\{v\in V\mid v\bot E_{k-1}\}$
+\begin_inset Formula $E_{k-1}^{\bot}\coloneqq \{v\in V\mid v\bot E_{k-1}\}$
 \end_inset
 
 , basta ver que para todo subespacio 
@@ -1671,7 +1671,7 @@ Si
 \end_inset
 
  dada por 
-\begin_inset Formula $\Vert f\Vert:=\sqrt{\langle f,f\rangle}$
+\begin_inset Formula $\Vert f\Vert\coloneqq \sqrt{\langle f,f\rangle}$
 \end_inset
 
  define una norma en 
@@ -1845,7 +1845,7 @@ Entonces, para
 
 \begin_layout Standard
 Sea 
-\begin_inset Formula $A:=(a_{ij})_{ij}\in{\cal M}_{n}(\mathbb{C})$
+\begin_inset Formula $A\coloneqq (a_{ij})_{ij}\in{\cal M}_{n}(\mathbb{C})$
 \end_inset
 
 :
@@ -2028,7 +2028,7 @@ La
 norma euclídea
 \series default
 , 
-\begin_inset Formula $\Vert A\Vert_{E}:=\sqrt{\sum_{i,j}|a_{ij}|^{2}}$
+\begin_inset Formula $\Vert A\Vert_{E}\coloneqq \sqrt{\sum_{i,j}|a_{ij}|^{2}}$
 \end_inset
 
 , es una norma matricial no subordinada a ninguna norma en 
@@ -2150,7 +2150,7 @@ Sea
 
 \begin_layout Standard
 Sea 
-\begin_inset Formula $D_{\delta}:=\text{diag}(1,\delta,\dots,\delta^{n-1})$
+\begin_inset Formula $D_{\delta}\coloneqq \text{diag}(1,\delta,\dots,\delta^{n-1})$
 \end_inset
 
  para 
@@ -2202,7 +2202,7 @@ La diagonal no cambia, la matriz sigue siendo triangular superior y, para
 
 .
  Tomando la norma 
-\begin_inset Formula $\Vert v\Vert_{*}:=\Vert(UD_{\delta})^{-1}v\Vert_{\infty}$
+\begin_inset Formula $\Vert v\Vert_{*}\coloneqq \Vert(UD_{\delta})^{-1}v\Vert_{\infty}$
 \end_inset
 
 , la norma subordinada a esta cumple 
@@ -2353,7 +2353,7 @@ Demostración:
 \end_inset
 
 , sea 
-\begin_inset Formula $B_{\varepsilon}:=\frac{B}{\rho(B)+\varepsilon}$
+\begin_inset Formula $B_{\varepsilon}\coloneqq \frac{B}{\rho(B)+\varepsilon}$
 \end_inset
 
 , se tiene 
@@ -2510,7 +2510,7 @@ número de condición
 \end_inset
 
  a 
-\begin_inset Formula $\text{cond}A:=\Vert A\Vert\Vert A^{-1}\Vert$
+\begin_inset Formula $\text{cond}A\coloneqq \Vert A\Vert\Vert A^{-1}\Vert$
 \end_inset
 
 , con lo que si 
@@ -2556,7 +2556,7 @@ número de condición
 
 \begin_layout Standard
 Llamamos 
-\begin_inset Formula $\text{cond}_{p}(A):=\Vert A^{-1}\Vert_{p}\Vert A\Vert_{p}$
+\begin_inset Formula $\text{cond}_{p}(A)\coloneqq \Vert A^{-1}\Vert_{p}\Vert A\Vert_{p}$
 \end_inset
 
 .
@@ -2654,7 +2654,7 @@ Sean
 \end_inset
 
  invertible con 
-\begin_inset Formula $D:=P^{-1}AP=:\text{diag}(\lambda_{i})$
+\begin_inset Formula $D\coloneqq P^{-1}AP=:\text{diag}(\lambda_{i})$
 \end_inset
 
 , 
@@ -2666,7 +2666,7 @@ Sean
 \end_inset
 
  para toda matriz diagonal y 
-\begin_inset Formula $D_{i}:=B(\lambda_{i},\text{cond}(P)\Vert\Delta A\Vert)\subseteq\mathbb{C}$
+\begin_inset Formula $D_{i}\coloneqq B(\lambda_{i},\text{cond}(P)\Vert\Delta A\Vert)\subseteq\mathbb{C}$
 \end_inset
 
 ,