File:Gershgorin Disk Theorem Example.svg
Summary
| Description |
English: Gershgorin disk theorem example. This diagram shows the discs in yellow derived for the eigenvalues. The first two disks overlap and their union contains two eigenvalues. The third and fourth disks are disjoint from the others and contain one eigenvalue each. |
| Date | |
| Source | Own work |
| Author | Nicoguaro |
| SVG development | |
| Source code | Python codeimport numpy as np
import matplotlib.pyplot as plt
# Graph setup
yellow = "#e9eabb"
blue = "#122a8c"
gray = '#757575'
plt.rcParams["text.color"] = gray
plt.rcParams["font.size"] = 12
plt.rcParams["xtick.color"] = gray
plt.rcParams["ytick.color"] = gray
plt.rcParams["axes.labelcolor"] = gray
plt.rcParams["axes.edgecolor"] = gray
plt.rcParams["axes.spines.right"] = False
plt.rcParams["axes.spines.top"] = False
A = np.array([
[10, -1, 0, 1],
[0.2, 8, 0.2, 0.2],
[1, 1, 2, 1],
[-1, -1, -1, -11]])
vals = np.linalg.eigvals(A)
fig = plt.figure(figsize=(6, 4))
for cont, val in enumerate(vals):
real = np.real(val)
imag = np.imag(val)
center = A[cont, cont]
radius = sum(np.abs(A[cont, k]) for k in range(4) if k != cont)
circle = plt.Circle((center, 0), radius, color=yellow)
plt.plot(real, imag, color=blue, marker="x", linewidth=0)
plt.gca().add_artist(circle)
plt.legend(["Eigenvalues"], frameon=False)
plt.xlabel("Real axis")
plt.ylabel("Imaginary axis")
plt.yticks([-10, -5, 0, 5, 10])
plt.axis("image")
plt.xlim(-15, 15)
plt.ylim(-10, 10)
plt.savefig("Gershgorin Disk Theorem Example.svg", bbox_inches="tight")
plt.show()
|
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