r/LinearAlgebra

Can anyone help me with my Gaussian Elimination algorithm?

why is my Gaussian Elimination algorithm doesn't work, especially the second part, I made a lot more details on why I think it doesn't here https://scicomp.stackexchange.com/questions/45561/gaussian-elimination-2nd-part but I can't get it completely. can anyone help?

import numpy as np

A=np.array([[4,8,12],[3,8,13],[2,9,18]])
b=np.array([4,5,11])

def Gauss_Elimination(A,b):
    n = np.shape(A)[0]

    # 1st Part
    for k in range(n):
        pivot_element=A[k,k]
        # if pivot_element==0: ### I'll deal with this condition later
        for j in range(k+1,n):
            b[j]=b[j]-(A[j,k]/pivot_element)*b[k]
            A[j,:]=A[j,:]-(A[j,k]/pivot_element)*A[k,:]

        # 2nd Part
        x = np.zeros(n)
        x[-1]=b[-1]/A[-1,-1]
        for i in range(n-2,-1,-1):
        x[i]=(b[i]-np.sum(x[i+1]-A[i,i+1]))/A[i,i]
    return A,b, x # not necessary since it's call by reference

Gauss_Elimination(A,b)
print(A,'\n',b)

reddit.com

u/Mental_Primary_5558 — 4 days ago

▲ 14 r/LinearAlgebra

3D visualizer for Linear Algebra

Recently i started learning Linear Algebra, din`t learn on University,
Now i`m feeling useful again.
I created this application using Python, ThreeJS on PySide6

Is a plotter 3D, i`m making a for creating notebooks, like TeX with plotter, help me to understand the logics

u/will_be_over_soon — 6 days ago

▲ 15 r/LinearAlgebra

I made a video explaining Choi matrices and how linear algebra helps us understand quantum channels

Hey everyone! I recently made a video explaining Choi matrices, complete positivity, and quantum channels.

If you're studying linear algebra and are curious about how concepts like eigenvalues, positive semidefinite matrices, tensor products, and the trace are used in quantum computing, I thought this might be interesting!

I work through several examples step by step, including how a matrix can have a negative eigenvalue and what that tells us about whether a quantum operation is physically valid.

Thought I'd share since it's a nice real-world application of linear algebra!

Happy to hear any feedback or suggestions!

youtu.be

u/dogpup3 — 6 days ago

▲ 48 r/LinearAlgebra+1 crossposts

New Free Mini-Course: Proofs in Elementary Linear Algebra

Hey folks! I am starting a new mini-course on proofs in elementary linear algebra. The target audience is primarily those students who have taken a computation based linear algebra course and now are transitioning to a proof-based linear algebra course. Instead of developing linear algebra theory, we will focus on constructing proofs and writing proofs. Consequently we won't develop the theory much beyond elementary properties of linear transformations.

I am planning to follow Chapter 17 of Chartrand-Polimeni-Zhang; this is an "online only" chapter and is available at https://media.pearsoncmg.com/cmg/pmmg_mml_shared/Chartrand_4e/index.html . I will specifically solve as many problems from there as possible.

If this sounds like something you would benefit from following, here is the github repo I'll be using as the course webpage:

https://github.com/AlpUzman/Proofs_in_Elementary_Linear_Algebra

And I'll add the episodes to the following Youtube playlist:

https://www.youtube.com/playlist?list=PL40ydqvvyXfMwFmNvppWUuE3sgOP1RI5-

On Github so far there is only the 'sittybos' (Greek equivalent of 'syllabus'). I have recorded the first episode already, and I am planning to finish post-production and release it on my Youtube channel in about a week. The mini-course will be freely available on my Youtube channel, with a new episode every other week (tentatively).

I am also attaching a random still from episode 1 as a teaser.

Thanks!

u/AlpUzman — 13 days ago