File:Gershgorin Disk Theorem Example.svg
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DescriptionGershgorin Disk Theorem Example.svg |
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 InfoField | This plot was created with Matplotlib. |
Source code InfoField | 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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I, the copyright holder of this work, hereby publish it under the following license:
This file is licensed under the Creative Commons Attribution 4.0 International license.
- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
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Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 19:44, 15 February 2019 | 503 × 344 (24 KB) | Nicoguaro (talk | contribs) | User created page with UploadWizard |
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Height | 274.946563pt |