September 2024
Intermediate to advanced
328 pages
8h 54m
Spanish
Content preview from Álgebra lineal práctica para la ciencia de datos
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Capítulo 8. Matriz inversa
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Pasamos a resolver ecuaciones matriciales. Las ecuaciones matriciales son como las ecuaciones normales (por ejemplo, resolver x en 4x = 8) pero... tienen matrices. A estas alturas del libro, ya sabes que las cosas se complican cuando intervienen las matrices. No obstante, debemos aceptar esa complejidad, porque resolver ecuaciones matriciales es una parte enorme de la ciencia de datos.
La inversa de la matriz es fundamental para resolver ecuaciones matriciales en aplicaciones prácticas, incluido el ajuste de modelos estadísticos a los datos (piensa en los modelos lineales generales y la regresión). Al final de este capítulo, sabrás qué es la inversa de una matriz, cuándo se puede calcular y cuándo no, cómo calcularla y cómo interpretarla.
La Matriz Inversa
La inversa de la matriz es otra matriz (pronunciada "A inversa") que multiplica a para producir la matriz identidad. Dicho de otro modo . Así es como se "cancela" una matriz. Otra conceptualización es que queremos transformar linealmente una matriz en la matriz identidad; la matriz inversa contiene esa transformación lineal, y la multiplicación de matrices es el mecanismo de aplicar esa transformación a la matriz.
Pero, ¿por qué necesitamos invertir matrices? Necesitamos "cancelar" una matriz para resolver problemas que pueden expresarse de la forma
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