wingedrasengan927/linear-algebra

Implementations, Expts, Notes, and problems of various linear algebra concepts from many resources but mainly from the book "No bu@@@it guide to linear algebra" by Ivan Savov

linear-algebra

Notes, Ideas, Problems, Experiments on various linear algebra concepts mainly from the book "no bull---t guide to linear algebra" by Ivan Savov and many other resources

Breakdown of Concepts

Vectors

Includes Basics of Vectors, Vector operations like addition, subtraction, dot product, cross product, projections onto other vectors; Implementation of a vector class using numpy.

• Vectors

Matrices

Includes basics of Matrix Operations like addition, subtraction, multiplication, finding determinants and inverse, Implemented manually and using SymPy Library.

• Matrices

Solving System of Equations

Includes Gauss-Jordan Elimination process visualizing solution to system of equations in 2D and 3D, and Cramers Rule for solving system of equations

• System of Equations

Geometric Linear Algebra

Includes Representation of lines, planes, determinants; projection onto vectors, planes; distilling and finding basis, null space, row space, column space;

• Geometric Linear Algebra

Linear Transformations

Includes problems on linear transformations and representing Matrices as a linear transformation

• Linear Transformations

Abstract Vector Spaces

Includes representation of a Matrix as a vector, and problems on Gram-Schimdt Orthogonalization

• Abstract Vector Spaces

Eigen Decomposition and Eigen Vectors

Includes problems on Eigendecomposition and Eigenvectors solved manually, and using the SymPy library.

• Eigen Decomposition and Eigen Vectors

Singular Value Decomposition

Includes application of SVD, Notes, Articles and Papers

• Great Medium Article
• Great Paper

Notes

• The beauty of Orthonormal Eigen Vectors of a Matrix
• Notes from the above princeton paper

SVD Applications

• Image Approximation and Visualizing different components of the matrix
• Noise reduction