Course curriculum

  • 1

    Introduction

    • Course Introduction

    • Why Learn Linear Algebra?

    • Linear Algebra Defined

    • Numerical Linear Algebra

    • Linear Algebra and Statistics

  • 2

    NumPy

    • NumPy Array Defined

    • Functions to Create Arrays

    • Combining Arrays

    • From Lists to Arrays

    • Indexing Arrays

    • Slicing Arrays (Important Lesson)

    • Reshaping Arrays

    • Array Broadcasting

    • Demo: Array Broadcasting

    • Demo: Array Broadcasting Limitations

  • 3

    Matrices

    • Vectors

    • Demo: Vector Arithmetic

    • Demo: Vector Dot Product

    • Matrices

    • Defining, Adding and Subtracting a Matrix

    • Matrix Multiplication and Division

    • Matrix-Matrix Multiplication (Dot Product)

    • Matrix Scalar Multiplication

    • Matrix Operations: Transpose

    • Matrix Operations: Inversion

    • Matrix Operations: Trace and Determinant

    • Matrix Operations: Rank

    • Matrix Types: Square and Symmetric

    • Matrix Types: Triangular and Diagonal

    • Matrix Types: Identity and Orthogonal Matrix

    • Spare Matrix

    • Problems with Sparsity

    • Sparse Matrices in Machine Learning

    • Matrix Sparsity in Python

    • Tensors

    • Tensors in Python

    • Tensor Dot Product

  • 4

    Factorization

    • Matrix Decomposition

    • Matrix Decomposition: LU

    • Matrix Decomposition: QR and Cholesky

    • Eigenvectors and Eigenvalues

    • Calculation of Eigen Decomposition

    • Confirm and Reconstruct Eigenvector

    • Singular-Value Decomposition

    • Reconstruct Matrix from SVD

    • SVD for Dimensionality Reduction