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.
Course content
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Video class: Advanced Linear Algebra 1: Vector Spaces
0h41m
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Exercise: What is a critical assumption when checking if a subset of a vector space is also a vector space?
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Video class: Advanced Linear Algebra 2: Spans
0h46m
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Exercise: What concept ensures polynomials are a vector space?
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Video class: Advanced Linear Algebra 3: Bases
0h47m
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Exercise: What is the standard basis for R3?
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Video class: Advanced Linear Algebra 4: Dimension of a Vector Space
0h48m
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Exercise: What determines linear independence of vectors in R4?
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Video class: Advanced Linear Algebra 5: Change of Basis
0h48m
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Exercise: Matrix Transformation in Polynomial Vector Spaces
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Video class: Advanced Linear Algebra 6: Linear Transformations
0h40m
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Exercise: What is the underlying concept of linear algebra emphasized in the video?
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Video class: Advanced Linear Algebra 7: Properties of Linear Transformations
0h41m
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Exercise: What is the result of a linear transformation on polynomials of degree up to 3 when applying the derivative twice?
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Video class: Advanced Linear Algebra 8: The Half Derivative
0h42m
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Exercise: What is the half derivative of sine of x?
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Video class: Advanced Linear Algebra 9: Isomorphic Vector Spaces
0h45m
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Exercise: Which vector spaces are isomorphic?
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Video class: Advanced Linear Algebra 10: Linear Forms
0h48m
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Exercise: Identify the Dot Product Example
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Video class: Advanced Linear Algebra 11: Bilinear Forms
0h50m
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Exercise: Properties of Bilinear Forms
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Video class: Advanced Linear Algebra 12: The Inner Product
0h48m
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Exercise: What are the properties of the dot product in linear algebra?
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Video class: Advanced Linear Algebra 13: Norm, Triangle Inequality, Orthogonality
0h48m
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Exercise: What is the main focus of an inner product space?
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Video class: Advanced Linear Algebra 14: Orthogonal Basis
0h47m
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Exercise: What is an Orthonormal Basis?
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Video class: Advanced Linear Algebra 15: Gram-Schmidt
0h48m
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Exercise: What is the main goal of the Gram-Schmidt process?
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Video class: Advanced Linear Algebra 16: Adjoint of Linear Transformation
0h47m
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Exercise: What is the concept of the transpose of a matrix associated with in linear algebra?
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Video class: Advanced Linear Algebra 17: Schur's Unitary Triangularization
0h44m
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Exercise: What describes the form of the matrix A after the linear transformation involving eigenvalues?
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Video class: Advanced Linear Algebra 18: Normal Matrices
0h49m
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Exercise: Which condition must a complex matrix satisfy to be diagonalizable with a unitary matrix?
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Video class: Advanced Linear Algebra 19: Real Spectral Theorem
0h43m
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Exercise: How can you ensure real decompositions from a real matrix?
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Video class: Advanced Linear Algebra 20: Positive Definite
0h46m
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Exercise: What conditions must a matrix satisfy to be used in defining an inner product over complex numbers?
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.
Linear Algebra is a cornerstone of higher mathematics and is widely applicable in fields such as engineering, physics, computer science, and economics. Understanding this subject can open doors to numerous career opportunities and academic advancements. Our selection of free courses ensures that you can learn without the burden of financial constraints.
Why Choose Our Free Linear Algebra Courses?
- Comprehensive Content: Covering all essential topics including vector spaces, linear transformations, matrix theory, and eigenvalues.
- Expert Instructors: Learn from top educators and professionals in the field.
- Flexible Learning: Study at your own pace with self-paced courses.
- Interactive Learning: Engage with interactive modules, quizzes, and problem sets.
- Certification: Some courses offer certificates of completion to boost your resume.
Featured Free Linear Algebra Courses
- Introduction to Linear Algebra - A beginner-friendly course covering the basics of linear algebra, including vectors, matrices, and systems of linear equations.
- Advanced Linear Algebra - Dive deeper into advanced topics such as eigenvalues, eigenvectors, and diagonalization.
- Linear Algebra for Data Science - Learn how linear algebra is applied in data science, machine learning, and artificial intelligence.
- Practical Linear Algebra - Focus on real-world applications of linear algebra in engineering, physics, and computer science.
- Linear Algebra and Optimization - Explore the intersection of linear algebra and optimization techniques used in various industries.
Each of these courses is designed to provide you with a robust understanding of Linear Algebra, tailored to your specific interests and career goals. By choosing free courses, you can access high-quality education without the financial burden. Start your journey today and unlock the potential of Linear Algebra in your academic and professional life.
Don't miss out on the opportunity to learn from the best and gain valuable skills that are highly sought after in today's job market. Enroll in one or more of these free Linear Algebra courses and take the first step towards mastering this essential mathematical discipline.
For more courses and resources in Algebra, visit our Algebra Courses section.
Advanced Algebra
This free course includes:
23 hours and 1 minutes of online video course
Exercises to train your knowledge
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