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+#LyX 2.3 created this file. For more info see http://www.lyx.org/
+\lyxformat 544
+\begin_document
+\begin_header
+\save_transient_properties true
+\origin unavailable
+\textclass book
+\use_default_options true
+\maintain_unincluded_children false
+\language spanish
+\language_package default
+\inputencoding auto
+\fontencoding global
+\font_roman "default" "default"
+\font_sans "default" "default"
+\font_typewriter "default" "default"
+\font_math "auto" "auto"
+\font_default_family default
+\use_non_tex_fonts false
+\font_sc false
+\font_osf false
+\font_sf_scale 100 100
+\font_tt_scale 100 100
+\use_microtype false
+\use_dash_ligatures true
+\graphics default
+\default_output_format default
+\output_sync 0
+\bibtex_command default
+\index_command default
+\paperfontsize default
+\spacing single
+\use_hyperref false
+\papersize default
+\use_geometry false
+\use_package amsmath 1
+\use_package amssymb 1
+\use_package cancel 1
+\use_package esint 1
+\use_package mathdots 1
+\use_package mathtools 1
+\use_package mhchem 1
+\use_package stackrel 1
+\use_package stmaryrd 1
+\use_package undertilde 1
+\cite_engine basic
+\cite_engine_type default
+\biblio_style plain
+\use_bibtopic false
+\use_indices false
+\paperorientation portrait
+\suppress_date false
+\justification true
+\use_refstyle 1
+\use_minted 0
+\index Index
+\shortcut idx
+\color #008000
+\end_index
+\secnumdepth 3
+\tocdepth 3
+\paragraph_separation indent
+\paragraph_indentation default
+\is_math_indent 0
+\math_numbering_side default
+\quotes_style french
+\dynamic_quotes 0
+\papercolumns 1
+\papersides 1
+\paperpagestyle default
+\tracking_changes false
+\output_changes false
+\html_math_output 0
+\html_css_as_file 0
+\html_be_strict false
+\end_header
+
+\begin_body
+
+\begin_layout Standard
+\begin_inset ERT
+status open
+
+\begin_layout Plain Layout
+
+
+\backslash
+begin{sloppypar}
+\end_layout
+
+\end_inset
+
+En Octave, todos los valores son matrices.
+ Los números (con sintaxis 
+\family typewriter
+[-+]?((
+\backslash
+d+
+\backslash
+.?|
+\backslash
+d*
+\backslash
+.
+\backslash
+d+)([eE][-+]?
+\backslash
+d+)?|[Ii]nf)
+\family default
+ o 
+\family typewriter
+(
+\family default
+{número}
+\family typewriter
+
+\backslash
++)?
+\family default
+{número}
+\family typewriter
+?i
+\family default
+) representan matrices 
+\begin_inset Formula $1\times1$
+\end_inset
+
+ de números de doble precisión, y las cadenas de caracteres (con sintaxis
+ 
+\family typewriter
+'([^']|'')*'
+\family default
+ o 
+\family typewriter
+"([^
+\backslash
+
+\backslash
+']|
+\backslash
+
+\backslash
+
+\family default
+{escape}
+\family typewriter
+)*"
+\family default
+) representan matrices fila de caracteres.
+\begin_inset ERT
+status open
+
+\begin_layout Plain Layout
+
+
+\backslash
+end{sloppypar}
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+La expresión 
+\family typewriter
+[
+\begin_inset Formula $a_{1}$
+\end_inset
+
+, 
+\family default
+...
+\family typewriter
+, 
+\begin_inset Formula $a_{p}$
+\end_inset
+
+]
+\family default
+ concatena horizontalmente las matrices 
+\begin_inset Formula $a_{1}\in{\cal M}_{m\times n_{1}}(S)$
+\end_inset
+
+ hasta 
+\begin_inset Formula $a_{p}\in{\cal M}_{m\times n_{p}}(S)$
+\end_inset
+
+ en una matriz en 
+\begin_inset Formula ${\cal M}_{m\times\sum_{k=1}^{p}n_{k}}(S)$
+\end_inset
+
+, y la sintaxis 
+\family typewriter
+[
+\begin_inset Formula $a_{11}$
+\end_inset
+
+, 
+\family default
+...
+\family typewriter
+, 
+\begin_inset Formula $a_{1p_{1}}$
+\end_inset
+
+; 
+\family default
+...
+\family typewriter
+; 
+\begin_inset Formula $a_{q1}$
+\end_inset
+
+, 
+\family default
+...
+\family typewriter
+, 
+\begin_inset Formula $a_{qp_{q}}$
+\end_inset
+
+]
+\family default
+ hace esto en cada parte, resultando en 
+\begin_inset Formula $q$
+\end_inset
+
+ matrices 
+\begin_inset Formula $b_{k}\in{\cal M}_{m_{k}\times n}(S)$
+\end_inset
+
+, y las concatena verticalmente en una 
+\begin_inset Formula ${\cal M}_{\sum_{k=1}^{q}m_{k}\times n}(S)$
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+El operador 
+\family typewriter
++
+\family default
+ suma matrices numéricas de igual tamaño y 
+\family typewriter
+*
+\family default
+ multiplica matrices o una matriz por un escalar.
+ Llamamos vector a una matriz fila.
+ Entonces 
+\family typewriter
+\emph on
+a
+\emph default
+:
+\emph on
+b
+\family default
+\emph default
+ genera el vector 
+\begin_inset Formula $(a,a+1,\dots,b)$
+\end_inset
+
+ y 
+\family typewriter
+\emph on
+a
+\emph default
+:
+\emph on
+t
+\emph default
+:
+\emph on
+b
+\family default
+\emph default
+ genera el vector 
+\begin_inset Formula $(a,a+t,\dots,b)$
+\end_inset
+
+.
+ Cuando es posible, 
+\family typewriter
+
+\begin_inset Formula $A$
+\end_inset
+
+
+\backslash
+
+\begin_inset Formula $B$
+\end_inset
+
+
+\family default
+ devuelve una matriz 
+\begin_inset Formula $X$
+\end_inset
+
+ tal que 
+\begin_inset Formula $AX=B$
+\end_inset
+
+.
+ 
+\family typewriter
+
+\begin_inset Formula $A$
+\end_inset
+
+'
+\family default
+ devuelve 
+\begin_inset Formula $A^{*}$
+\end_inset
+
+.
+ 
+\end_layout
+
+\begin_layout Standard
+
+\family typewriter
+\emph on
+A
+\emph default
+(
+\emph on
+x
+\emph default
+, 
+\emph on
+y
+\emph default
+)
+\family default
+ devuelve la submatriz de 
+\family typewriter
+\emph on
+A
+\family default
+\emph default
+ formada por las columnas con índice en el vector 
+\family typewriter
+\emph on
+x
+\family default
+\emph default
+ y las filas con índice en el vector 
+\family typewriter
+\emph on
+y
+\family default
+\emph default
+, y 
+\family typewriter
+\emph on
+A
+\emph default
+(
+\emph on
+x
+\emph default
+)
+\family default
+ convierte la matriz en un vector concatenando las traspuestas de sus columnas
+ y toma los elementos del vector con índice en el vector 
+\family typewriter
+\emph on
+x
+\family default
+\emph default
+.
+ Ambos vectores se pueden sustituir por 
+\family typewriter
+:
+\family default
+ para tomar todas las filas o columnas, y los índices empiezan por 1.
+ 
+\end_layout
+
+\begin_layout Standard
+Las expresiones son sentencias, y estas deben terminar por salto de línea
+ si se quiere que se imprima su resultado o por 
+\family typewriter
+;
+\family default
+, seguido opcionalmente de salto de línea, si no.
+ La sentencia 
+\family typewriter
+\emph on
+A
+\emph default
+ = 
+\emph on
+expr
+\family default
+\emph default
+ asigna a la variable 
+\family typewriter
+\emph on
+A
+\family default
+\emph default
+ el valor 
+\family typewriter
+\emph on
+expr
+\family default
+\emph default
+, y 
+\family typewriter
+\emph on
+A
+\emph default
+(
+\emph on
+x
+\emph default
+, 
+\emph on
+y
+\emph default
+) = 
+\emph on
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+\family default
+\emph default
+ o 
+\family typewriter
+\emph on
+A
+\emph default
+(
+\emph on
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+\emph default
+) = 
+\emph on
+expr
+\family default
+\emph default
+ asigna los elementos de la submatriz a la izquierda del 
+\family typewriter
+=
+\family default
+ a los de la devuelta por la expresión, que debe ser del mismo tamaño.
+ Si la variable no existe, se crea, y si la submatriz indicada supone que
+ 
+\family typewriter
+\emph on
+A
+\family default
+\emph default
+ es más grande, esta se amplía y se rellena con ceros.
+\end_layout
+
+\begin_layout Section
+Funciones sobre matrices
+\end_layout
+
+\begin_layout Description
+
+\family typewriter
+cond(
+\series bold
+\emph on
+A
+\series default
+\emph default
+,
+\emph on
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+)
+\family default
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+norm(
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+\emph on
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+\emph default
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+\emph default
+)
+\family default
+.
+\end_layout
+
+\begin_layout Description
+
+\family typewriter
+cond(
+\series bold
+\emph on
+A
+\series default
+\emph default
+)
+\family default
+ 
+\family typewriter
+cond(
+\emph on
+A
+\emph default
+,2)
+\family default
+.
+\end_layout
+
+\begin_layout Description
+
+\family typewriter
+diag(
+\emph on
+A
+\emph default
+,
+\emph on
+k
+\emph default
+)
+\family default
+ Si 
+\family typewriter
+\emph on
+A
+\family default
+\emph default
+ es vector, devuelve una matriz diagonal con elementos del vector en la
+ diagonal, y de lo contrario devuelve un vector con los elementos de la
+ diagonal de 
+\family typewriter
+\emph on
+A
+\family default
+\emph default
+.
+\end_layout
+
+\begin_layout Description
+
+\family typewriter
+dot(
+\emph on
+x
+\emph default
+,
+\emph on
+y
+\emph default
+)
+\family default
+ Producto escalar hermitiano 
+\begin_inset Formula $\langle\text{\emph{\texttt{y}}},\text{\emph{\texttt{x}}}\rangle$
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Description
+
+\family typewriter
+[
+\emph on
+V
+\emph default
+,
+\emph on
+lambda
+\emph default
+]=eig(
+\emph on
+A
+\emph default
+)
+\family default
+ Devuelve una matriz diagonal 
+\family typewriter
+\emph on
+lambda
+\family default
+\emph default
+ en la que los elementos de la diagonal son los valores propios de 
+\family typewriter
+\emph on
+A
+\family default
+\emph default
+ y una matriz 
+\family typewriter
+\emph on
+V
+\family default
+\emph default
+ cuyas columnas son los vectores propios correspondientes.
+\end_layout
+
+\begin_layout Description
+
+\family typewriter
+eye(
+\emph on
+n
+\emph default
+)
+\family default
+ Matriz identidad de tamaño 
+\family typewriter
+\emph on
+n
+\family default
+\emph default
+.
+\end_layout
+
+\begin_layout Description
+
+\family typewriter
+inv(
+\emph on
+A
+\emph default
+)
+\family default
+ Inversa de la matriz cuadrada no singular 
+\family typewriter
+\emph on
+A
+\family default
+\emph default
+.
+\end_layout
+
+\begin_layout Description
+
+\family typewriter
+linspace(
+\emph on
+start
+\emph default
+,
+\emph on
+end
+\emph default
+,
+\emph on
+n
+\emph default
+)
+\family default
+ Vector de 
+\family typewriter
+\emph on
+n
+\family default
+\emph default
+ puntos equiespaciados de 
+\family typewriter
+\emph on
+start
+\family default
+\emph default
+ a 
+\family typewriter
+\emph on
+end
+\family default
+\emph default
+.
+\end_layout
+
+\begin_layout Description
+
+\family typewriter
+norm(
+\emph on
+A
+\series medium
+\emph default
+,
+\emph on
+p
+\emph default
+)
+\family default
+ Norma 
+\family typewriter
+\series default
+\emph on
+p
+\family default
+\emph default
+ de 
+\family typewriter
+\emph on
+A
+\family default
+\emph default
+, matricial o vectorial según corresponda, donde 
+\family typewriter
+\emph on
+p
+\family default
+\emph default
+ es un entero positivo o 
+\family typewriter
+Inf
+\family default
+.
+ 
+\end_layout
+
+\begin_layout Description
+
+\family typewriter
+norm(
+\emph on
+A
+\emph default
+)
+\family default
+ 
+\family typewriter
+norm(
+\emph on
+A
+\emph default
+,2)
+\family default
+.
+\end_layout
+
+\begin_layout Description
+
+\family typewriter
+rand(
+\emph on
+m
+\emph default
+,
+\emph on
+n
+\emph default
+)
+\family default
+ Matriz de 
+\family typewriter
+\emph on
+m
+\family default
+\emph default
+ filas y 
+\family typewriter
+\emph on
+n
+\family default
+\emph default
+ columnas con elementos aleatorios entre 0 y 1.
+\end_layout
+
+\begin_layout Description
+
+\family typewriter
+[
+\emph on
+U
+\emph default
+,
+\emph on
+S
+\emph default
+,
+\emph on
+V
+\emph default
+]=svd(
+\emph on
+A
+\emph default
+)
+\family default
+ Devuelve dos matriz ortogonales 
+\family typewriter
+\emph on
+U
+\family default
+\emph default
+ y 
+\family typewriter
+\emph on
+V
+\family default
+\emph default
+ y una diagonal 
+\family typewriter
+\emph on
+S
+\family default
+\emph default
+ tales que 
+\begin_inset Formula $\text{\emph{\texttt{A}}}=\text{\emph{\texttt{U}}}\text{\emph{\texttt{S}}}\text{\emph{\texttt{V}}}^{*}$
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Description
+
+\family typewriter
+trace(
+\emph on
+A
+\emph default
+)
+\family default
+ Traza de 
+\family typewriter
+\emph on
+A
+\family default
+\emph default
+.
+\end_layout
+
+\begin_layout Description
+
+\family typewriter
+tril(
+\emph on
+A
+\emph default
+,
+\emph on
+k
+\emph default
+)
+\family default
+ Matriz como 
+\family typewriter
+\emph on
+A
+\family default
+\emph default
+ pero con los elementos 
+\begin_inset Formula $(i,j)$
+\end_inset
+
+ con 
+\begin_inset Formula $j-i>\text{\emph{\texttt{k}}}$
+\end_inset
+
+ a 0.
+\end_layout
+
+\begin_layout Description
+
+\family typewriter
+tril(
+\emph on
+A
+\emph default
+)
+\family default
+ 
+\family typewriter
+tril(
+\emph on
+A
+\emph default
+,0)
+\family default
+, matriz triangular inferior.
+\end_layout
+
+\begin_layout Description
+
+\family typewriter
+triu(
+\emph on
+A
+\emph default
+,
+\emph on
+k
+\emph default
+)
+\family default
+ Matriz como 
+\family typewriter
+\emph on
+A
+\family default
+\emph default
+ pero con los elementos 
+\begin_inset Formula $(i,j)$
+\end_inset
+
+ con 
+\begin_inset Formula $i-j>\text{\emph{\texttt{k}}}$
+\end_inset
+
+ a 0.
+\end_layout
+
+\begin_layout Description
+
+\family typewriter
+triu(
+\emph on
+A
+\series bold
+\emph default
+)
+\family default
+\series default
+ 
+\family typewriter
+triu(
+\emph on
+A
+\emph default
+,0)
+\family default
+, matriz triangular superior.
+\end_layout
+
+\begin_layout Description
+
+\family typewriter
+zeros(
+\emph on
+m
+\emph default
+,
+\emph on
+n
+\emph default
+)
+\family default
+ Matriz nula de 
+\family typewriter
+\emph on
+m
+\family default
+\emph default
+ filas y 
+\family typewriter
+\emph on
+n
+\family default
+\emph default
+ columnas.
+\end_layout
+
+\end_body
+\end_document