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# 33.1: Descomposición Matriz

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%matplotlib inline
import matplotlib.pylab as plt
import numpy as np
import sympy as sym
sym.init_printing(use_unicode=True)
##### Hacer esto

Mira el siguiente video y responde las preguntas a continuación.

from IPython.display import YouTubeVideo
YouTubeVideo("-_2he4J6Xxw",width=640,height=360, cc_load_policy=True)

Considera el siguiente código para calcular la$$A = Q\Lambda Q^{-1}$$ eivendecomposition.

# Here is our input matrix
A = np.matrix([[15,7,-7],[-1,1,1],[13,7,-5]])
sym.Matrix(A)
# Calculate eigenvalues and vectors using Numpy
e, Q = np.linalg.eig(A)
print(e)
sym.Matrix(Q)
#Turn eigenvalues into a diagonal matrix  (there is even a function for that!)
L = np.diag(e)
sym.Matrix(L)
# Calculate A again from Q and L

A2 = Q*L*np.linalg.inv(Q)

sym.Matrix(A2)
##### Hacer esto

Usando código, verifique que A2 sea lo mismo que$$A$$.

# Put your answer here
##### Hacer esto

Convierte el código anterior en una función llamada eigendecomp que toma una matriz A y devuelve Q y L.

# Put your code here
##### Pregunta

¿Qué otras descomposiciones hemos cubierto en la clase hasta ahora? Haz una lista y escribe una breve descripción de por qué usamos cada descomposición.

This page titled 33.1: Descomposición Matriz is shared under a CC BY-NC 4.0 license and was authored, remixed, and/or curated by Dirk Colbry via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.