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MANE 3351

Lecture 24

Classroom Management

Agenda

  • Linear Algebra using software
  • Homework 7 (assigned 11/24/25, due 12/1/25 - no late submissions)
  • Turn in Raspberry Pi and Arduino

Resources

Handouts

Calendar

Week Monday Lecture Wednesday Lecture
14 12/1: Lecture 24 - Software 12/3: Lecture 25 - Review
15 12/8: Lecture 26 - no class 12/10: Lecture 27 - no class

Final Exam is Monday 12/15/2025 8:00 - 9:45 AM

I will be off-campus on an ABET visit and a proctor will be arranged for the final exam.

Assignments

  • Homework 7 (assigned 11/40, due 12/1 - no late submissions)

Solving Linear Algebra using Python/Jupyter Notebook

  • Slides prepared by ChatGPT
  • Options: NumPy, SciPy, SymPy, scikit-learn, CVXPY, PyTorch, TensorFlow, Jax, GNU Octave

NumPy

  • Core package for numerical computing

  • Supports vectors, matrices, broadcasting

  • Linear algebra routines via numpy.linalg

  • Matrix multiplication

  • Eigenvalues/eigenvectors

  • Determinants

  • Solving linear systems

SciPy

  • Builds on NumPy with advanced algorithms

  • scipy.linalg for optimized linear algebra

  • Supports sparse matrices via scipy.sparse

  • Interfaces with LAPACK / BLAS

  • Advanced solvers (iterative, sparse solvers)

SymPy

  • Symbolic mathematics engine

  • Exact arithmetic (non-floating point)

  • Matrix algebra:

    • Inverse, rank, determinant

    • Eigenvalues symbolically

    • Jordan normal form

  • Useful for teaching and derivations

scikit-learn

  • Machine learning library built on NumPy/SciPy

  • Uses linear algebra heavily for:

    • PCA

    • SVD

    • Least-squares models

  • Efficient sparse matrix utilities

CVXPY

  • Convex optimization modeling library

  • Expresses problems using linear algebra primitives

  • Solves:

    • LP, QP

    • QCQP, SOCP

    • SDP (semidefinite programs)

  • Works with NumPy/SciPy as backend

PyTorch

  • GPU-accelerated tensor computation

  • Automatic differentiation

  • Linear algebra routines:

    • Matrix multiplication

    • Solve linear systems

    • Decompositions: SVD, QR, Cholesky

TensorFlow

  • Large-scale tensor computing

  • GPU/TPU support

  • tf.linalg includes:

    • Determinant

    • Matrix inverse

    • SVD / QR

    • Matrix solve

  • Automatic differentiation support

JAX

  • NumPy-compatible high-performance computing

  • JIT compilation via XLA

  • Autodiff built in

  • jax.numpy.linalg for fast linear algebra

  • Excellent for simulation, optimization, ML research

GNU Octave

  • MATLAB-compatible numerical computing environment

  • Supports vectors, matrices, advanced linear algebra

  • Key features:

    • Built-in solvers for linear systems (A\b)

    • Eigenvalue/eigenvector computations

    • Matrix decompositions: LU, QR, SVD

    • Symbolic math via optional packages

  • Jupyter Support:

    • Can be used through the Octave Kernel for Jupyter notebooks

    • Integrates smoothly into teaching workflows

  • Excellent for users transitioning between MATLAB and Python

Example Problems (Generated by ChatGPT)

A= $$ \begin{bmatrix} 2 & 1 & -1 \ -1 & 3 & 2 \ 3 & -2 & 4 \end{bmatrix} $$

x= $$ \mathbf{x} = \begin{bmatrix} x \ y \ z \end{bmatrix} $$

b= $$ \begin{bmatrix} 3 \ 4 \ 5 \end{bmatrix} $$

C= $$ \begin{bmatrix} 1 & 2 \ 0 & 1 \ 3 & -1 \end{bmatrix} $$

Jupyter Demonstration 1 - Numpy

Jupyter Demonstration 2 - SciPy

Octave

GNU Octave is an open-source, MATLAB-compatible numerical computing environment used for:

  • Linear algebra
  • Numerical analysis
  • Simulation & modeling
  • Signal processing
  • Optimization
  • Teaching & engineering computations

Octave syntax is highly similar to MATLAB, making it ideal for students and engineers who want a free alternative.

Key Features

  • Fully MATLAB-compatible language (scripts & functions)
  • Powerful matrix operations and linear algebra tools
  • Built-in solvers (A\b, pinv, eig, svd, qr, etc.)
  • Supports plotting and visualization (plot, surf, etc.)
  • Interactive command-line and GUI
  • Works inside Jupyter Notebooks via the Octave Kernel

Installing GNU Octave & Jupyter Notebook Support (Windows)

Download & Install GNU Octave

  1. Go to the official Octave download page: 👉 https://octave.org/download
  2. Under Windows, download the latest .exe installer.
  3. Run the installer:
  4. Accept default settings
  5. Ensure Add Octave to system PATH is selected (if available)
  6. Launch Octave to verify installation.

Install the Octave Kernel for Jupyter

In Anaconda Prompt (or cmd):

A. Install via pip
pip install octave_kernel
B. Install Octave support (oct2py)
pip install oct2py
C. Verify kernel installation
python -m octave_kernel.check

You should see Octave executable found.

Jupyter Demonstration 3 - Octave within Jupyter Notebook