https://github.com/madhavjivrajani/linearalgebra
Assignment for UE18MA251, Linear Algebra
https://github.com/madhavjivrajani/linearalgebra
equations factorize gaussian linearalgebra matplotlib python
Last synced: 18 days ago
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Assignment for UE18MA251, Linear Algebra
- Host: GitHub
- URL: https://github.com/madhavjivrajani/linearalgebra
- Owner: MadhavJivrajani
- Created: 2020-02-05T14:21:46.000Z (over 6 years ago)
- Default Branch: master
- Last Pushed: 2020-03-15T08:23:36.000Z (over 6 years ago)
- Last Synced: 2026-04-08T05:29:25.375Z (3 months ago)
- Topics: equations, factorize, gaussian, linearalgebra, matplotlib, python
- Language: Jupyter Notebook
- Size: 81.1 KB
- Stars: 0
- Watchers: 1
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
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README
# LinearAlgebra
Assignments for UE18MA251, Linear Algebra
Coded purely from scratch using Python 3.6.x.
## Assignment - 1
Given a matrix A for the system of equations `Ax = b`
- Display, number of equations/rows, number of unknowns/columns, and rank of the matrix. (Use built in functions if required)
- Is the matrix singular (if it is a square matrix)?
- For a given `b`, will the system `Ax = b` have
- Unique solution.
- Infinitely many solutions
- No Solution.
- If it has a unique solution display the solution.
## Assignment 2
- For a given matrix A which has a unique solution for Ax=b for any b,
test whether the LU factorization method is faster than the Gaussian Elimination method.
Run a test in this manner:
- First read a matrix A with full rank/full column rank.
- Generate a hundred random b vectors.
- Find a solution for each b.
- Note down how long this approach takes.
- Factorize A to LU.
- Generate a hundred random b vectors.
- Find a solution for each b.
- Record how long does this new approach take.
Check if the claim that the first approach takes `100*O(n3/3 )` and the second approach takes `O(n3/3 ) + 99*O(n2)` is true.