Special Topics in Linear Algebra
This course covers the fundamentals of linear algebra and least squares approximation. It begins with an introduction to linear algebra and the fundamental theorem. It then moves on to fitting data to a straight curve, including linear regression and polynomial regression. Finally, it covers the application of least squares approximation to solve problems. ▼
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Course Feature
Cost:
Free
Provider:
Youtube
Certificate:
Paid Certification
Language:
English
Start Date:
On-Demand
Course Overview
❗The content presented here is sourced directly from Youtube platform. For comprehensive course details, including enrollment information, simply click on the 'Go to class' link on our website.
Updated in [February 21st, 2023]
Linear Algebra - Least Squares Approximation - 01 - Introduction.
Linear Algebra - Least Squares Approximation - 02 - Fundamental Theorem.
Linear Algebra - Least Squares Approximation - 03 - Fitting data to a straight curve Part 1.
Linear Algebra - Least Squares Approximation - 04 - Fitting data to a straight curve Part 2.
Linear Algebra - Least Squares Approximation - 05 - Fitting data to a straight curve Part 3.
Linear Algebra - Least Squares Approximation - 06 - Fitting data to a straight curve example.
Linear Algebra - Least Squares Approximation - 07 - Fitting data to more general functions.
Linear Algebra - Least Squares Approximation - 08 - The inverse of A transpose times A.
Linear Algebra - Hamming's error correcting codes - 01 - Hamming matrices.
Linear Algebra - Hamming's error correcting codes - 02 - Properties of Hamming matrices.
Linear Algebra - Hamming's error correcting codes - 03 - Example.
Linear Algebra - Hamming's error correcting codes - 04 - Parity bits.
Topics in Linear Algebra - The Functional Calculus - 01 - Theorem and Example.
Topics in Linear Algebra - The Functional Calculus - 02 - Square-root of a positive matrix.
Topics in Linear Algebra - The Functional Calculus - 03 - Polynomial interpolation.
Topics in Linear Algebra - The Functional Calculus - 04 - The determinant of a Vandermonde matrix.
Topics in Linear Algebra - The Functional Calculus - 05 - Proof of main theorem.
Affine subspaces and transformations - 01 - affine combinations.
Affine subspaces and transformations - 02 - affine subspaces.
Affine subspaces and transformations - 03 - affine transformations.
Affine subspaces and transformations - 04 - composition of affine transformations.
Stochastic maps - 01 - Conditional probabilities.
Stochastic maps - 02 - Composing conditional probabilities.
Stochastic maps - 03 - Products of conditional probabilities and a.e. equivalence.
Stochastic maps - 04 -Bayes' theorem.
Finite-dimensional C*-algebras - 01 - *-homomorphisms.
Finite-dimensional C*-algebras - 02 - positivity.
Finite-dimensional C*-algebras - 03 - Stochastic Gelfand--Naimark theorem.
(Please note that we obtained the following content based on information that users may want to know, such as skills, applicable scenarios, future development, etc., combined with AI tools, and have been manually reviewed)
What skills and knowledge will you acquire during this course?
By taking this online course, learners will acquire a comprehensive understanding of Special Topics in Linear Algebra, including Least Squares Approximation, Hamming's Error Correcting Codes, the Functional Calculus, Affine Subspaces and Transformations, Stochastic Maps, and Finite-dimensional C*-algebras. Learners will gain the ability to apply these concepts to real-world problems, analyze data, solve equations, and develop algorithms. Additionally, learners will be able to use the concepts of linear algebra to develop models and simulations. These skills and knowledge can be applied to various career paths, such as Data Scientist, Machine Learning Engineer, and Quantitative Analyst.
How does this course contribute to professional growth?
This online course provides learners with a comprehensive overview of Special Topics in Linear Algebra, from Least Squares Approximation to Finite-dimensional C*-algebras. Learners will gain a better understanding of the fundamentals of linear algebra, as well as the ability to apply these concepts to real-world problems. Through this course, learners will be able to develop the skills necessary to pursue a career in data science, machine learning engineering, and quantitative analysis. Additionally, learners will be able to use the techniques learned in this course to analyze data, solve equations, and develop algorithms. This course will thus contribute to professional growth by providing learners with the skills and knowledge necessary to pursue a career in these fields.
Is this course suitable for preparing further education?
This online course provides a comprehensive overview of Special Topics in Linear Algebra, from Least Squares Approximation to Finite-dimensional C*-algebras. Learners will gain a better understanding of the fundamentals of linear algebra, as well as the ability to apply these concepts to real-world problems. This course provides learners with the skills and knowledge necessary to pursue a career in data science, machine learning engineering, or quantitative analysis.
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