May 1, 2024
Updated May 8, 2025
23 minute read
Eigenvalues, at a high level, are special numbers associated with a set of linear equations (a matrix) that characterize its properties. Think of a matrix as a transformation in space – stretching, rotating, or shearing. Eigenvalues tell you about the "strength" or "magnitude" of that transformation along specific directions, known as eigenvectors. If you're new to linear algebra, this might sound a bit abstract, but eigenvalues are fundamental concepts with surprisingly broad applications. You might find it engaging to see how these mathematical constructs can describe real-world phenomena, from the stability of a bridge to the energy levels of an atom in quantum mechanics. The power of eigenvalues also shines in data analysis, where they help uncover hidden patterns and reduce complex information into more manageable forms.
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Reading list
We've selected 12 books
that we think will supplement your
learning. Use these to
develop background knowledge, enrich your coursework, and gain a
deeper understanding of the topics covered in
Eigenvalues.
This classic textbook offers a comprehensive treatment of matrix theory, including a thorough discussion of eigenvalues and eigenvectors, and is suitable for advanced undergraduates or graduate students.
This undergraduate textbook presents a rigorous and modern treatment of linear algebra, including a thorough discussion of eigenvalues and eigenvectors, and is known for its clear and engaging writing style.
Provides an in-depth exploration of eigenvalues and eigenvectors from a geometric perspective, offering a unique and visually appealing approach to understanding the concepts.
Explores the interplay between graph theory and eigenvalues, providing a deep understanding of the spectral properties of graphs, which are essential for applications in network analysis and data science.
Covers the emerging field of tensor networks and its applications in quantum information theory, including a discussion of the role of eigenvalues and eigenvectors in understanding quantum entanglement.
Covers numerical methods for linear algebra, including algorithms for computing eigenvalues and eigenvectors, and is suitable for students and researchers in scientific computing and engineering.
Explores the theory and applications of stochastic matrices, which are matrices with nonnegative elements and row sums equal to one, including a discussion of eigenvalues and eigenvectors in the context of Markov chains.
This open-source textbook covers eigenvalues and eigenvectors as part of its comprehensive treatment of linear algebra, making it a valuable resource for gaining a broad understanding of the topic.
For more information about how these books relate to this course, visit:
OpenCourser.com/topic/zvbfrd/eigenvalue
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