Eigenvalues, Eigenvectors and Diagonalization of Matrices - Linear Algebra (Undergraduate Advanced)

This course provides a clear and structured exploration of eigenvalues, eigenvectors, and diagonalization, focusing on both theory and real-world applications. You’ll learn how to compute eigenvalues and eigenvectors, understand their geometric significance, and apply diagonalization to simplify complex matrix operations. Topics include linear transformations, dynamical systems, and applications in physics, engineering, and machine learning. The course is designed for students, engineers, and data scientists seeking a strong foundation in matrix methods. By the end, you'll confidently apply these concepts in problem-solving and computational modeling.

17 hrs

Enrolment valid for 12 months
This course is also part of the following learning tracks. You may join a track to gain comprehensive knowledge across related courses.
MTH 202: Mathematical Methods II
MTH 202: Mathematical Methods II
Comprehensive treatise of advanced mathematics covering vector calculus, complex numbers, linear vector spaces, linear maps, matrices, eigenvalues and eigenvectors. Curated for second-year students of engineering and physical sciences at Obafemi Awolowo University, Ile-Ife, Nigeria. Students and professionals with similar learning goal will also find this learning track useful.

Comprehensive treatise of advanced mathematics covering vector calculus, complex numbers, linear vector spaces, linear maps, matrices, eigenvalues and eigenvectors. Curated for second-year students of engineering and physical sciences at Obafemi Awolowo University, Ile-Ife, Nigeria. Students and professionals with similar learning goal will also find this learning track useful.

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CHE 305: Engineering Analysis I
CHE 305: Engineering Analysis I
Advanced engineering mathematics covering solid analytical geometry, integrals, scalar and vector fields, matrices and determinants and complex variables. Curated for third-year students of engineering at Obafemi Awolowo University, Ile-Ife, Nigeria. Students and professionals with similar learning goal will also find this learning track useful.

Advanced engineering mathematics covering solid analytical geometry, integrals, scalar and vector fields, matrices and determinants and complex variables. Curated for third-year students of engineering at Obafemi Awolowo University, Ile-Ife, Nigeria. Students and professionals with similar learning goal will also find this learning track useful.

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MTH 205: Linear Algebra II
MTH 205: Linear Algebra II
Advanced linear algebra is the mathematical backbone of modern data science, engineering, and physics. This learning track delivers the rigorous MTH 205 curriculum based on NUC CCMAS standards, focusing on sophisticated matrix analysis and practical computational methods critical for solving complex technical problems. This programme is targeted at undergraduates in mathematics, engineering, and computer science requiring a deep command of advanced matrix theory. It is equally essential for data scientists and engineers seeking a rigorous theoretical foundation for machine learning algorithms, cryptography, and complex system modelling. You will master matrix manipulations to solve linear systems and compute determinants and inverses efficiently using various methods including software like Python and MATLAB. You will gain competence in determining eigenvalues and eigenvectors, applying diagonalization to analyze the stability of dynamical systems, and working with quadratic and canonical forms. Completion establishes the critical mathematical expertise required for advanced studies in multivariate statistics, differential equations, and algorithmic development.

Advanced linear algebra is the mathematical backbone of modern data science, engineering, and physics. This learning track delivers the rigorous MTH 205 curriculum based on NUC CCMAS standards, focusing on sophisticated matrix analysis and practical computational methods critical for solving complex technical problems. This programme is targeted at undergraduates in mathematics, engineering, and computer science requiring a deep command of advanced matrix theory. It is equally essential for data scientists and engineers seeking a rigorous theoretical foundation for machine learning algorithms, cryptography, and complex system modelling. You will master matrix manipulations to solve linear systems and compute determinants and inverses efficiently using various methods including software like Python and MATLAB. You will gain competence in determining eigenvalues and eigenvectors, applying diagonalization to analyze the stability of dynamical systems, and working with quadratic and canonical forms. Completion establishes the critical mathematical expertise required for advanced studies in multivariate statistics, differential equations, and algorithmic development.

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Course Chapters

1. Introduction
2
Welcome and course outline. Review of elementary matrix concepts.
Concept Overviews
2 Lessons
48:34
2. Eigenvalues and Eigenvectors
9
2
Meaning, operations and properties of eigenvalues and eigenvectors of matrices.
Concept Overviews
9 Lessons
3:11:35
Problem Walkthroughs
2 Lessons
1:28:46
3. Diagonalization of Matrices
6
2
Diagonalization of matrices; evaluating polynomials and transcendentals of matrices.
Concept Overviews
6 Lessons
1:50:25
Problem Walkthroughs
2 Lessons
1:00:53
4. Symmetric Matrices
3
2
Diagonalization of symmetric matrices - orthogonal diagonalizing matrix, the Gram-Schmidt orthogonalization procedure, and related concepts.
Concept Overviews
3 Lessons
1:31:36
Problem Walkthroughs
2 Lessons
1:20:43
5. Quadratic and Canonical Forms
4
2
Quadratic and canonical forms; transformations using symmetric matrices and orthogonal diagonalizing matrices.
Concept Overviews
4 Lessons
1:04:11
Problem Walkthroughs
2 Lessons
1:20:01