Free online courseAdvanced Linear Algebra

Duration of the online course: 23 hours and 1 minutes

New course

Explore Advanced Linear Algebra with Andrews University. Discover vector spaces, transformations, and real-world applications in finance, neural networks, and more.

Course Description

Delve deep into Advanced Linear Algebra with this comprehensive online course from Andrews University, tailored to elevate your understanding of complex algebraic concepts. This course is essential for anyone seeking to expand their knowledge in algebra and related fields, incorporating a detailed exploration of vector spaces, transformations, and matrix functions.

Discover the intricacies of vector spaces, exploring spans, bases, and dimensions that are fundamental to building a solid algebraic foundation. Progress to change of basis and delve into the mechanics of linear transformations and their properties. Engage with advanced topics such as the half derivative and explore the concept of isomorphic vector spaces.

The course further investigates linear and bilinear forms, touching on the vital concepts of inner products, norms, and orthogonality. Master techniques like the Gram-Schmidt process and understand the importance of an orthogonal basis in solving complex algebraic problems.

Advanced learners can challenge themselves with units on the adjoint of linear transformations and Schur's unitary triangularization. The curriculum extends to normal matrices and the real spectral theorem, providing insights into positive definite matrices and their applications.

Explore polar and singular value decompositions, followed by an analysis of Frobenius and operator norms. Take on the stimulating task of finding blocks of the Jordan decomposition and understanding the broader framework of the Jordan decomposition generalized eigenspace.

Courses on functions of matrices, including exponential and trigonometric functions, prepare students for practical applications across various disciplines. Gain an edge in mathematics and related fields with topics on tensors, Markov chains in finance, epidemiology, and page ranking. The inclusion of linear algebra in neural networks and spectral clustering emphasizes real-world applications, bridging theoretical concepts with practical solutions.

Conteúdo do Curso

  • Video class: Advanced Linear Algebra 1: Vector Spaces

    0h41m

  • Exercise: What is a critical assumption when checking if a subset of a vector space is also a vector space?

  • Video class: Advanced Linear Algebra 2: Spans

    0h46m

  • Exercise: What concept ensures polynomials are a vector space?

  • Video class: Advanced Linear Algebra 3: Bases

    0h47m

  • Exercise: What is the standard basis for R3?

  • Video class: Advanced Linear Algebra 4: Dimension of a Vector Space

    0h48m

  • Exercise: What determines linear independence of vectors in R4?

  • Video class: Advanced Linear Algebra 5: Change of Basis

    0h48m

  • Exercise: Matrix Transformation in Polynomial Vector Spaces

  • Video class: Advanced Linear Algebra 6: Linear Transformations

    0h40m

  • Exercise: What is the underlying concept of linear algebra emphasized in the video?

  • Video class: Advanced Linear Algebra 7: Properties of Linear Transformations

    0h41m

  • Exercise: What is the result of a linear transformation on polynomials of degree up to 3 when applying the derivative twice?

  • Video class: Advanced Linear Algebra 8: The Half Derivative

    0h42m

  • Exercise: What is the half derivative of sine of x?

  • Video class: Advanced Linear Algebra 9: Isomorphic Vector Spaces

    0h45m

  • Exercise: Which vector spaces are isomorphic?

  • Video class: Advanced Linear Algebra 10: Linear Forms

    0h48m

  • Exercise: Identify the Dot Product Example

  • Video class: Advanced Linear Algebra 11: Bilinear Forms

    0h50m

  • Exercise: Properties of Bilinear Forms

  • Video class: Advanced Linear Algebra 12: The Inner Product

    0h48m

  • Exercise: What are the properties of the dot product in linear algebra?

  • Video class: Advanced Linear Algebra 13: Norm, Triangle Inequality, Orthogonality

    0h48m

  • Exercise: What is the main focus of an inner product space?

  • Video class: Advanced Linear Algebra 14: Orthogonal Basis

    0h47m

  • Exercise: What is an Orthonormal Basis?

  • Video class: Advanced Linear Algebra 15: Gram-Schmidt

    0h48m

  • Exercise: What is the main goal of the Gram-Schmidt process?

  • Video class: Advanced Linear Algebra 16: Adjoint of Linear Transformation

    0h47m

  • Exercise: What is the concept of the transpose of a matrix associated with in linear algebra?

  • Video class: Advanced Linear Algebra 17: Schur's Unitary Triangularization

    0h44m

  • Exercise: What describes the form of the matrix A after the linear transformation involving eigenvalues?

  • Video class: Advanced Linear Algebra 18: Normal Matrices

    0h49m

  • Exercise: Which condition must a complex matrix satisfy to be diagonalizable with a unitary matrix?

  • Video class: Advanced Linear Algebra 19: Real Spectral Theorem

    0h43m

  • Exercise: How can you ensure real decompositions from a real matrix?

  • Video class: Advanced Linear Algebra 20: Positive Definite

    0h46m

  • Exercise: What conditions must a matrix satisfy to be used in defining an inner product over complex numbers?

Linear algebra

Free online courses on Linear algebra

Free Linear Algebra Courses

Are you looking to enhance your mathematical skills with a focus on Linear Algebra? You've come to the right place! Our curated list of free Linear Algebra courses will help you master concepts such as vector spaces, matrices, eigenvalues, and more. Whether you're a student, a professional, or a math enthusiast, these courses offer comprehensive content to suit your learning needs.

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For more courses and resources in Algebra, visit our Algebra Courses section.

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23 hours and 1 minutes of online video course

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