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# Online course Linear Algebra IV: Orthogonality & Symmetric Matrices and the SVD

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## Linear Algebra IV: Orthogonality & Symmetric Matrices and the SVD

Unlock the advanced principles of linear algebra. Dive deep into the critical concepts of orthogonality, symmetric matrices, and singular value decomposition (SVD), essential for mastering higher-level mathematics and applications in various fields. Enroll today and empower your academic and professional pursuits with cutting-edge linear algebra knowledge!

### What will I learn?

The online orthogonal algebra course (in its free or paid mode), Linear Algebra IV: Orthogonality & Symmetric Matrices and the SVD, is a specialized journey into the realms of orthogonality, symmetric matrices, and Singular Value Decomposition (SVD). You will explore the advanced topics of linear algebra that are crucial for data science, machine learning, and engineering. By the end of this course, you will have a robust understanding of orthogonality, symmetric matrices, and SVD, equipping you with the tools to tackle advanced mathematical challenges.

This course is designed for those who have a foundational understanding of linear algebra and are ready to explore these advanced concepts. Students who are enrolling in this class should have completed the previous course in our four-part linear algebra sequence: Linear Algebra III. The course has a rigorous and didactic approach, which combines clear and simple explanations with examples and activities that will help you consolidate your learning. The course also offers you additional resources, such as readings, videos and links of interest, that you can consult to expand your knowledge and deepen the topics that interest you the most.

This course is available on the edX platform, one of the world’s most prestigious online education platforms, founded by MIT and Harvard University. It can be taken completely free of charge or for a small fee.

### Contents of the online orthogonal algebra course, Linear Algebra IV: Orthogonality & Symmetric Matrices and the SVD

These are the contents of the course:

1. Introduction to Orthogonality: Learn the fundamentals of orthogonality, including orthogonal vectors and orthogonal projections, and understand their importance in simplifying complex problems.
2. Orthogonal Matrices: Explore the properties and applications of orthogonal matrices, and discover how they preserve vector norms and angles, making them useful in various transformations.
3. Symmetric Matrices: Understand the unique properties of symmetric matrices, including their eigenvalues and eigenvectors, and how they arise in numerous practical applications.
4. Spectral Theorem: Delve into the spectral theorem for symmetric matrices, which provides a powerful tool for diagonalizing matrices and simplifying quadratic forms.
5. Singular Value Decomposition (SVD): Master the SVD, a key factorization technique used in many applications such as signal processing, statistics, and machine learning.
6. Applications of SVD: Discover practical applications of SVD in areas such as image compression, data reduction, and solving linear systems, enhancing your problem-solving skills.

### Paid or free orthogonal algebra course

The course has two modalities: free and paid. The free orthogonal algebra course, allows you to access all the content of the course, including the videos, the readings, the exercises and the discussion forums.

The paid modality also offers you the possibility of obtaining a verified certificate from edX, which accredits your participation and approval of the course. This certificate can be of great value for your curriculum vitae, as it demonstrates your interest and competence in orthogonal algebra. In addition, by paying for the course, you will be contributing to The Georgia Institute of Technology and edX being able to continue offering quality and accessible courses for everyone. If you want to know more about the cost and benefits of this modality, I invite you to visit the course page on edX, where you will find all the information you need.

In conclusion, the online orthogonal algebra course (in its free or paid mode), Linear Algebra IV: Orthogonality & Symmetric Matrices and the SVD, will not only deepen your understanding of linear algebra but also enhance your ability to apply these concepts to real-world problems. With a focus on practical application and theoretical depth, you’ll emerge with a skill set that is highly valued in fields such as data science, engineering, and computer graphics. Enroll now and take your algebraic knowledge to new heights!

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