1.1: Definición de una Matriz
- Page ID
- 119147
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Una matriz\(m\) -by- es una\(n\) matriz rectangular de números (u otros objetos matemáticos) con\(m\) filas y\(n\) columnas. Por ejemplo, una matriz de dos por dos\(\text{A}\), con dos filas y dos columnas, parece
\[\text{A}=\left(\begin{array}{cc}a&b\\c&d\end{array}\right).\nonumber \]
(A veces se usan corchetes en lugar de paréntesis). La primera fila tiene elementos\(a\) y\(b\), la segunda fila tiene elementos\(c\) y\(d\). La primera columna tiene elementos\(a\) y\(c\); la segunda columna tiene elementos\(b\) y\(d\). Como ejemplos adicionales, las\(2\) matrices\(2\) -by-\(3\) y\(3\) -by- parecen
\[\text{B}=\left(\begin{array}{ccc}a&b&c\\d&e&f\end{array}\right),\quad \text{C}=\left(\begin{array}{cc}a&b\\c&d\\e&f\end{array}\right).\nonumber \]
De especial importancia son las llamadas matrices de filas y matrices de columna. Estas matrices también se denominan vectores de fila y vectores de columna. El vector fila es en general\(1\) -by-\(n\) y el vector de columna es\(n\) -by-\(1\). Por ejemplo, cuando\(n = 3\), escribiríamos
\[\text{v}=\left(\begin{array}{ccc}a&b&c\end{array}\right)\nonumber \]
como vector de fila, y
\[\text{v}=\left(\begin{array}{c}a\\b\\c\end{array}\right)\nonumber \]
como un vector de columna.