[{"data":1,"prerenderedAt":368},["Reactive",2],{"options:asyncdata:$ogpPUTwkW6:/p/orden-de-una-matriz-dimension-de-una-matriz:0":3},{"page":4,"book":25,"news":362,"questionSent":19,"questions":363,"formData":364,"attachments":22,"chartData":22,"pending":19,"chartOptions":365,"afspec":19,"aflink":367},{"id":5,"book_id":6,"chapter_id":7,"name":8,"slug":9,"html":10,"priority":11,"created_at":12,"updated_at":13,"created_by":14,"updated_by":18,"draft":19,"markdown":20,"revision_count":15,"template":19,"owned_by":21,"editor":20,"trends":22,"raw_html":23,"tags":24},4026,23,0,"Orden de una matriz (dimensión de una matriz)","orden-de-una-matriz-dimension-de-una-matriz","\u003Cp id=\"bkmrk-el-orden-de-una-matr\">El \u003Cstrong>orden de una matriz o dimensión de una matriz\u003C/strong> es el número \u003Cem>m\u003C/em> de filas y \u003Cem>n\u003C/em> de columnas que la componen, expresándose como matriz de orden o dimensión \\(m \\times n\\). Así, una matriz de orden o dimensión \\(3 \\times 2\\) tiene 3 filas y 2 columnas. \u003C/p>",35,"2026-02-21T16:28:02.000000Z","2026-03-09T08:59:35.000000Z",{"id":15,"name":16,"slug":17},1,"Admin","admin",{"id":15,"name":16,"slug":17},false,"",{"id":15,"name":16,"slug":17},null,"\u003Cp id=\"bkmrk-el-orden-de-una-matr\">El \u003Cstrong>orden de una matriz o dimensión de una matriz\u003C/strong> es el número \u003Cem>m\u003C/em> de filas y \u003Cem>n\u003C/em> de columnas que la componen, expresándose como matriz de orden o dimensión \\(m \\times n\\). Así, una matriz de orden o dimensión \\(3 \\times 2\\) tiene 3 filas y 2 columnas. \u003C/p>",[],{"id":6,"name":26,"slug":27,"description":20,"created_at":28,"updated_at":28,"created_by":15,"updated_by":15,"owned_by":15,"default_template_id":22,"pages":29,"index":60,"shelves":355},"Matemática general","matematica-general","2023-05-22T06:25:36.000000Z",[30,35,40,45,50,55],{"id":31,"name":32,"slug":33,"html":34},3291,"Intervalo cerrado","intervalo-cerrado","\u003Cp id=\"bkmrk-un%C2%A0intervalo-cerrado\">\u003Ca href=\"https://es.gizapedia.org/uploads/images/gallery/2025-06/FT04tIeo45GNPU4g-standalone-msa-figure-12-1.png\" target=\"_blank\" rel=\"noopener\">\u003Cimg class=\"align-right\" src=\"https://es.gizapedia.org/uploads/images/gallery/2025-06/scaled-1680-/FT04tIeo45GNPU4g-standalone-msa-figure-12-1.png\" alt=\"Standalone_MSA_Figure-12-1.png\" width=\"280\" height=\"150\">\u003C/a>Un \u003Cstrong>intervalo cerrado\u003C/strong> es un intervalo o conjunto de números reales definidos entre dos valores, que incuuye sus extremos. Se expresa mediante un par de números, los extremos menor y mayor, entre corchetes. Por ejemplo, el intervalo cerrado [1,3], incluye todos los números reales entre 1 y 3 incluyendo al 1 y al 3. \u003C/p>\r\n\u003Cp id=\"bkmrk-puede-interesarte-ta\">\u003Cstrong>Puede interesarte también\u003C/strong>\u003C/p>\r\n\u003Cul id=\"bkmrk-intervalo-abierto-in\">\r\n\u003Cli class=\"null\">\u003Ca href=\"https://ikusmira.org/p/intervalo-abierto\">\u003Cstrong>Intervalo abierto\u003C/strong>\u003C/a>\u003C/li>\r\n\u003Cli class=\"null\">\u003Cstrong>\u003Ca href=\"https://ikusmira.org/p/intervalo-mixto-intervalo-semiabierto-intervalo-semicerrado\">Intervalo mixto (intervalo semiabierto, intervalo semicerrado)\u003C/a>\u003C/strong>\u003C/li>\r\n\u003C/ul>",{"id":36,"name":37,"slug":38,"html":39},3350,"Trinomio","trinomio","\u003Cp id=\"bkmrk-un-trinomio-es-una-s\">Un\u003Cstrong> trinomio\u003C/strong> es una \u003Cstrong>\u003Ca href=\"https://ikusmira.org/p/expresion-algebraica\">expresión algebraica\u003C/a>\u003C/strong> resultado de la suma de tres \u003Cstrong>\u003Ca href=\"https://ikusmira.org/p/termino-algebraico\">términos algebraicos\u003C/a>\u003C/strong>, cada uno de los cuales es un producto de \u003Cstrong>\u003Ca href=\"https://ikusmira.org/p/constante-matematicas\">constantes \u003C/a>\u003C/strong>y variables, elevadas cada una de ellas a una potencia entera no negativa; se trata por tanto de un polinomio de tres términos. \u003C/p>\r\n\u003Cp id=\"bkmrk-ejemplos-de-trinomio\">\u003Cstrong>Ejemplos de trinomios\u003C/strong>\u003C/p>\r\n\u003Cul id=\"bkmrk-%5C%284x%5E2%2B2x%2B1%5C%29-%28trino\">\r\n\u003Cli class=\"null\">\\(4x^2+2x+1\\) (trinomio de segundo grado)\u003Cbr>\u003C/li>\r\n\u003Cli class=\"null\">4xy+2x+6y\u003C/li>\r\n\u003Cli class=\"null\">2mn+pq+2\u003C/li>\r\n\u003C/ul>\r\n\u003Cp id=\"bkmrk-puede-interesarte-ta\">\u003Cstrong>Puede interesarte también\u003C/strong>\u003C/p>\r\n\u003Cul id=\"bkmrk-monomio-binomio\">\r\n\u003Cli class=\"null\">\u003Ca href=\"https://ikusmira.org/p/monomio\">\u003Cstrong>Monomio\u003C/strong>\u003C/a>\u003C/li>\r\n\u003Cli class=\"null\">\u003Ca href=\"https://ikusmira.org/p/binomio-algebra\">\u003Cstrong>Binomio\u003C/strong>\u003C/a>\u003C/li>\r\n\u003C/ul>",{"id":41,"name":42,"slug":43,"html":44},102,"y=f(x)","yfx","\u003Cp id=\"bkmrk-la-expresi%C3%B3n-matem%C3%A1t\">La \u003Cstrong>expresión matemática \u003Cem>y=f(x)\u003C/em> \u003C/strong>indica la relación de dependencia que se establece entre una variable x y una variable y, de modo que a cada valor de la variable \u003Cem>x\u003C/em> le corresponde un único valor de la variable \u003Cem>y\u003C/em>. En matemáticas, \u003Cem>y=f(x)\u003C/em> denota lo que comúnmente se llama una función, y más estrictamente una aplicación. La variable \u003Cem>x\u003C/em> se denomina variable independiente, y la variable \u003Cem>y\u003C/em> variable independiente, ya que los valores de esta se hacen depender de aquella.\u003C/p>",{"id":46,"name":47,"slug":48,"html":49},2036,"Menores complementarios","menores-complementarios","\u003Cp id=\"bkmrk-en-algebra-lineal-y-\">En algebra lineal y en relación a un elemento de una matriz cuadrada, su \u003Cstrong>menor complementario\u003C/strong> es el determinante de la submatriz resultante de eliminar la fila y la columna correspondientes a ese elemento. Para un elemento \\(a_{ij}\\), se denomina \\(M(ij)\\).\u003C/p>\r\n\u003Cp id=\"bkmrk-ejemplo\">\u003Cstrong>Ejemplo\u003C/strong>\u003C/p>\r\n\u003Cp id=\"bkmrk-dada-la-siguiente-ma\">Dada la siguiente matriz,\u003Cbr>\u003C/p>\r\n\u003Cp id=\"bkmrk-%24%24%5Cleft-%28%5Cbegin%7Barra\">$$\\left (\u003Cbr>\\begin{array}{rrr}\u003Cbr>2 & 1 & 0 \\\\\u003Cbr>1 &-1 & 1 \\\\\u003Cbr>0 & 2 &-1\u003Cbr>\\end{array}\u003Cbr>\\right )$$\u003C/p>\r\n\u003Cp id=\"bkmrk-vamos-a-calcular-el-\">vamos a calcular el menor complementario correspondiente al elementos de la matriz $a_{11}=2$.\u003C/p>\r\n\u003Cp id=\"bkmrk-eliminamos-de-la-mat\">Eliminamos de la matriz la fila y columna correspondientes a dicho elemento, y formamos la submatriz resultante:\u003C/p>\r\n\u003Cp id=\"bkmrk-%24%24%5Cleft-%28%5Cbegin%7Barra-1\">$$\\left (\u003Cbr>\\begin{array}{rr}\u003Cbr>-1 & 1 \\\\\u003Cbr>2 &-1\u003Cbr>\\end{array}\u003Cbr>\\right )$$\u003C/p>\r\n\u003Cp id=\"bkmrk-el-menor-complementa\">El menor complementario de $a_11$ es el determinante de dicha submatriz:\u003C/p>\r\n\u003Cp id=\"bkmrk-%24%24m_%7B11%7D%3D%5Cleft-%7C%5Cbeg\">$$M_{11}=\\left |\u003Cbr>\\begin{array}{rr}\u003Cbr>-1 & 1 \\\\\u003Cbr>2 &-1\u003Cbr>\\end{array}\u003Cbr>\\right |=1 \\times -1 - 1 \\times 2=-3$$\u003C/p>\r\n\u003Cp id=\"bkmrk-los-menores-compleme\">Los menores complementarios deben calcularse como primer paso para el cálculo de la matriz inversa.\u003C/p>",{"id":51,"name":52,"slug":53,"html":54},4032,"Sistema homogéneo (álgebra lineal)","sistema-homogeneo-algebra-lineal","\u003Cp id=\"bkmrk-en-%C3%A1lgebra-lineal%2C-u\">En álgebra lineal, un \u003Cstrong>sistema homogéneo\u003C/strong> es un sistema de ecuaciones lineales en el que los términos independientes de todas la ecuaciones son 0, esto es, un sistema homogéneo es todo aque sistema que en notación matricial adopta la forma AX=0.\u003C/p>",{"id":56,"name":57,"slug":58,"html":59},1798,"Arista","arista","\u003Cp id=\"bkmrk-\">\u003Ca href=\"https://es.gizapedia.org/uploads/images/gallery/2024-03/ETLkwoAiRv9DEsM7-a-edge-in-a-cube.png\" target=\"_blank\" rel=\"noopener\">\u003Cimg src=\"https://es.gizapedia.org/uploads/images/gallery/2024-03/scaled-1680-/ETLkwoAiRv9DEsM7-a-edge-in-a-cube.png\" alt=\"A_edge_in_a_cube.png\" width=\"255\" height=\"255\">\u003C/a>\u003C/p>\r\n\u003Cp id=\"bkmrk-imagen%3A-arista-de-un\">\u003Cem>Imagen: Arista de un cubo, que une dos caras cuadradas, marcada con un segmento rojo. Créditos: A2569875,\u003Cspan class=\"mw-mmv-source-author\"> Commons.\u003C/span>\u003C/em>\u003C/p>\r\n\u003Cp id=\"bkmrk-una-arista-es-la-li%C3%AD\">Una \u003Cstrong>arista\u003C/strong> es la liínea de intersección entre dos planos. Referida a un poliedro o cuerpo geométrico de caras planas, es cada uno de los bordes de las caras del poliedro; en este caso, las aristas confluyen en un vértice. El término se utiliza también en teoría de grafos para denominar las líneas que unen dos vértices o nodos. \u003C/p>",{"":61},[62,66,70,72,77,82,87,92,97,102,107,112,117,122,127,132,137,142,147,152,155,160,165,170,174,179,181,186,191,196,201,206,211,216,218,223,224,229,234,239,244,249,254,259,264,269,274,279,281,286,291,296,298,303,308,313,318,323,328,330,335,340,345,350],{"id":63,"name":64,"slug":65,"priority":7,"chapter_name":22},3956,"Algoritmo","algoritmo",{"id":67,"name":68,"slug":69,"priority":15,"chapter_name":22},2552,"Anteperiodo de un número","anteperiodo-de-un-numero",{"id":56,"name":57,"slug":58,"priority":71,"chapter_name":22},2,{"id":73,"name":74,"slug":75,"priority":76,"chapter_name":22},829,"Base de cálculo","base-de-calculo",3,{"id":78,"name":79,"slug":80,"priority":81,"chapter_name":22},2069,"Binomio de Newton","binomio-de-newton",4,{"id":83,"name":84,"slug":85,"priority":86,"chapter_name":22},2573,"Clase de conjuntos","clase-de-conjuntos",5,{"id":88,"name":89,"slug":90,"priority":91,"chapter_name":22},2824,"Combinaciones con repetición (multicombinaciones)","combinaciones-con-repeticion-multicombinaciones",6,{"id":93,"name":94,"slug":95,"priority":96,"chapter_name":22},2814,"Combinaciones simples","combinaciones-simples",7,{"id":98,"name":99,"slug":100,"priority":101,"chapter_name":22},2764,"Conjunto vacío","conjunto-vacio",8,{"id":103,"name":104,"slug":105,"priority":106,"chapter_name":22},3799,"Constante (matemáticas)","constante-matematicas",9,{"id":108,"name":109,"slug":110,"priority":111,"chapter_name":22},3999,"Convergencia uniforme","convergencia-uniforme",10,{"id":113,"name":114,"slug":115,"priority":116,"chapter_name":22},3081,"Cuerpo conmutativo, campo (álgebra abstracta)","cuerpo-conmutativo-campo-algebra-abstracta",11,{"id":118,"name":119,"slug":120,"priority":121,"chapter_name":22},3200,"Diagonal secundaria (antidiagonal)","diagonal-secundaria-antidiagonal",12,{"id":123,"name":124,"slug":125,"priority":126,"chapter_name":22},2694,"Dimensión inductiva","dimension-inductiva",13,{"id":128,"name":129,"slug":130,"priority":131,"chapter_name":22},3346,"Discriminante (ecuaciones de segundo grado)","discriminante-ecuaciones-de-segundo-grado",14,{"id":133,"name":134,"slug":135,"priority":136,"chapter_name":22},4025,"Ecuación explícita de la recta","ecuacion-explicita-de-la-recta",15,{"id":138,"name":139,"slug":140,"priority":141,"chapter_name":22},3397,"Ecuaciones de primer grado","ecuaciones-de-primer-grado",16,{"id":143,"name":144,"slug":145,"priority":146,"chapter_name":22},4012,"Eje de abscisas","eje-de-abscisas",17,{"id":148,"name":149,"slug":150,"priority":151,"chapter_name":22},3869,"Expresión algebraica","expresion-algebraica",18,{"id":153,"name":149,"slug":150,"priority":154,"chapter_name":22},2313,19,{"id":156,"name":157,"slug":158,"priority":159,"chapter_name":22},2409,"Factorial","factorial",20,{"id":161,"name":162,"slug":163,"priority":164,"chapter_name":22},3800,"Función constante","funcion-constante",21,{"id":166,"name":167,"slug":168,"priority":169,"chapter_name":22},4024,"Función identidad","funcion-identidad",22,{"id":171,"name":172,"slug":173,"priority":6,"chapter_name":22},4088,"Función lineal","funcion-lineal",{"id":175,"name":176,"slug":177,"priority":178,"chapter_name":22},3293,"Intervalo abierto","intervalo-abierto",24,{"id":31,"name":32,"slug":33,"priority":180,"chapter_name":22},25,{"id":182,"name":183,"slug":184,"priority":185,"chapter_name":22},4059,"Intervalo mixto (intervalo semiabierto, intervalo semicerrado)","intervalo-mixto-intervalo-semiabierto-intervalo-semicerrado",26,{"id":187,"name":188,"slug":189,"priority":190,"chapter_name":22},3943,"Investigación operativa (investigación de operaciones)","investigacion-operativa-investigacion-de-operaciones",27,{"id":192,"name":193,"slug":194,"priority":195,"chapter_name":22},1129,"Línea poligonal","linea-poligonal",28,{"id":197,"name":198,"slug":199,"priority":200,"chapter_name":22},3223,"Líneas convergentes","lineas-convergentes",29,{"id":202,"name":203,"slug":204,"priority":205,"chapter_name":22},3224,"Líneas divergentes","lineas-divergentes",30,{"id":207,"name":208,"slug":209,"priority":210,"chapter_name":22},1034,"Líneas oblicuas (rectas oblicuas)","lineas-oblicuas-rectas-oblicuas",31,{"id":212,"name":213,"slug":214,"priority":215,"chapter_name":22},949,"Líneas paralelas (rectas paralelas)","lineas-paralelas-rectas-paralelas",32,{"id":46,"name":47,"slug":48,"priority":217,"chapter_name":22},33,{"id":219,"name":220,"slug":221,"priority":222,"chapter_name":22},2077,"Números redondos","numeros-redondos",34,{"id":5,"name":8,"slug":9,"priority":11,"chapter_name":22},{"id":225,"name":226,"slug":227,"priority":228,"chapter_name":22},3433,"Perímetro (geometría)","perimetro-geometria",36,{"id":230,"name":231,"slug":232,"priority":233,"chapter_name":22},777,"Periodo de un número","periodo-de-un-numero",37,{"id":235,"name":236,"slug":237,"priority":238,"chapter_name":22},3003,"Permutaciones circulares","permutaciones-circulares",38,{"id":240,"name":241,"slug":242,"priority":243,"chapter_name":22},2816,"Permutaciones con repetición","permutaciones-con-repeticion",39,{"id":245,"name":246,"slug":247,"priority":248,"chapter_name":22},2408,"Permutaciones simples","permutaciones-simples",40,{"id":250,"name":251,"slug":252,"priority":253,"chapter_name":22},2666,"Productorio","productorio",41,{"id":255,"name":256,"slug":257,"priority":258,"chapter_name":22},1773,"Punto medio","punto-medio",42,{"id":260,"name":261,"slug":262,"priority":263,"chapter_name":22},2914,"Puntos de corte (puntos de intersección)","puntos-de-corte-puntos-de-interseccion",43,{"id":265,"name":266,"slug":267,"priority":268,"chapter_name":22},2464,"Recta real","recta-real",44,{"id":270,"name":271,"slug":272,"priority":273,"chapter_name":22},2537,"Recta secante a una curva","recta-secante-a-una-curva",45,{"id":275,"name":276,"slug":277,"priority":278,"chapter_name":22},3021,"Rectas perpendiculares (rectas ortogonales)","rectas-perpendiculares-rectas-ortogonales",46,{"id":51,"name":52,"slug":53,"priority":280,"chapter_name":22},47,{"id":282,"name":283,"slug":284,"priority":285,"chapter_name":22},2800,"Subconjunto","subconjunto",48,{"id":287,"name":288,"slug":289,"priority":290,"chapter_name":22},2661,"Sumatorio","sumatorio",49,{"id":292,"name":293,"slug":294,"priority":295,"chapter_name":22},2037,"Término independiente (término constante)","termino-independiente-termino-constante",50,{"id":36,"name":37,"slug":38,"priority":297,"chapter_name":22},51,{"id":299,"name":300,"slug":301,"priority":302,"chapter_name":22},3625,"Valor (matemáticas)","valor-matematicas",52,{"id":304,"name":305,"slug":306,"priority":307,"chapter_name":22},926,"Valores consecutivos (números consecutivos)","valores-consecutivos-numeros-consecutivos",53,{"id":309,"name":310,"slug":311,"priority":312,"chapter_name":22},2821,"Variaciones con repetición","variaciones-con-repeticion",54,{"id":314,"name":315,"slug":316,"priority":317,"chapter_name":22},2815,"Variaciones simples","variaciones-simples",55,{"id":319,"name":320,"slug":321,"priority":322,"chapter_name":22},2676,"Vector (matemáticas)","vector-matematicas",56,{"id":324,"name":325,"slug":326,"priority":327,"chapter_name":22},3278,"Vector resultante","vector-resultante",57,{"id":41,"name":42,"slug":43,"priority":329,"chapter_name":22},58,{"id":331,"name":332,"slug":333,"priority":334,"chapter_name":22},4095,"Binomio (álgebra)","binomio-algebra",59,{"id":336,"name":337,"slug":338,"priority":339,"chapter_name":22},4098,"Monomio","monomio",60,{"id":341,"name":342,"slug":343,"priority":344,"chapter_name":22},4099,"Fracciones algebraicas","fracciones-algebraicas",61,{"id":346,"name":347,"slug":348,"priority":349,"chapter_name":22},4100,"Término algebraico","termino-algebraico",62,{"id":351,"name":352,"slug":353,"priority":354,"chapter_name":22},4123,"Diagonal principal","diagonal-principal",63,[356],{"id":71,"name":357,"slug":358,"description":20,"created_by":15,"updated_by":15,"created_at":359,"updated_at":360,"owned_by":15,"pivot":361},"Matemática y estadística","matematica-y-estadistica","2023-05-05T15:10:53.000000Z","2023-05-07T12:03:04.000000Z",{"book_id":6,"bookshelf_id":71},[],[],{"question":20,"name":20,"email":20,"page_id":5},{"responsive":366,"maintainAspectRatio":19},true,"https://www.amazon.es/hz/audible/mlp/mdp/discovery?actionCode=AMSTM1450129210001&tag=ikusmiraorg-21",1774088582013]