4.1 Introduction to Linear Algebra
Get familiar with matrices, vectors, and more as you explore the theory and real-world applications of linear algebra.
Two Linear Equations in Two Unknowns
Three Unknowns
Gaussian Elimination
The Full Story of Gaussian Elimination
Application: Kirchhoff and Circuits
Vector Spaces
Subspaces and Span
Linear Independence
Basis and Dimension
Dot Products and Inner Products
Least Squares
Matrix Algebra
Inverses and Systems of Equations
Four Fundamental Subspaces
Adjacency Matrices
Linear Transformations
Properties of Linear Transformations
2x2 Determinants
Determinants in Higher Dimensions
Representation by a Matrix
Change of Basis
Polynomial Interpolation
Eigenvalues and Eigenvectors
Characteristic Polynomial
Diagonalizability
PageRank and Exponentiation
Course description
Linear algebra is pervasive in just about all modern scientific subjects, including physics, mathematics, computer science, electrical engineering, economics, and aeronautical engineering. You’ll learn about its applications in computer graphics, signal processing, machine learning, RLC circuit analysis, and control theory. By the end of this course, you’ll be able to solve systems of equations of all flavors and complexities using linear algebra, from a simple 2x2 matrix equation to much more complex systems involving many variables.
Topics covered
- Bases
- Determinants
- Diagonalizable Matrices
- Dot products
- Eigenvalues and Eigenvectors
- Gaussian Elimination
- Inverses
- Linear Independence
- Linear Transformations
- Matrices
- Subspaces
- Vector Spaces
Prerequisites and next steps
A basic understanding of calculus and linear equations is necessary.
Prerequisites
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4.2 Linear Algebra with Applications
Delve into the abstract depths of linear algebra: vector spaces, determinants, eigenvalues, wedge products, and more.
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