May 1, 2024
Updated May 10, 2025
22 minute read
Gaussian elimination, also known as row reduction, is a fundamental algorithm in linear algebra used for solving systems of linear equations. It provides a systematic way to manipulate a system of equations, represented as a matrix, into a simpler form from which solutions can be readily obtained. This method is named after the renowned German mathematician Carl Friedrich Gauss, who, while not its sole discoverer, significantly formalized and popularized its use in the early 19th century. The technique's historical roots can even be traced back to ancient Chinese mathematics.
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Reading list
We've selected 19 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
Gaussian Elimination.
Provides a detailed analysis of the accuracy and stability of numerical algorithms, with significant coverage of Gaussian elimination. It valuable resource for understanding the nuances of the algorithm in finite precision arithmetic and is essential for researchers and professionals. It dives into contemporary topics and key reference.
This graduate-level textbook offers a concise yet insightful introduction to numerical linear algebra, covering Gaussian elimination and its stability. It provides a fresh perspective and is highly regarded for its clarity and focus on fundamental ideas. It's an excellent resource for deepening understanding at the graduate level.
This widely used textbook for a first course in linear algebra. It provides a strong foundation in the basics, including a clear explanation of Gaussian elimination and its applications. It is particularly useful for gaining a broad understanding and is often used as a primary textbook in undergraduate programs.
Another excellent introductory text by Gilbert Strang, this book also covers Gaussian elimination comprehensively. It is known for its clear explanations and focus on the fundamental concepts, making it suitable for high school and early undergraduate students seeking a broad understanding. It serves as a valuable resource for building foundational knowledge.
Focuses on the practical aspects of numerical linear algebra, including the implementation and analysis of Gaussian elimination. It is suitable for advanced undergraduate and graduate students and good reference for those interested in applying the concepts. It helps solidify understanding through practical application.
This textbook emphasizes a vectors approach to linear algebra and includes detailed explanations of Gaussian elimination. It is suitable for undergraduate students and helps bridge the gap between computational and theoretical aspects. It is often used as a textbook and provides a modern perspective.
Standard text for introductory linear algebra courses. It covers Gaussian elimination thoroughly with numerous examples and exercises, which is beneficial for solidifying understanding at the undergraduate level. It's a good reference for fundamental concepts and practice.
This comprehensive reference book on matrix theory. While not solely focused on Gaussian elimination, it provides in-depth coverage of related topics and advanced concepts essential for a deep understanding of matrix operations and their properties. It valuable resource for researchers and professionals.
Offers a clear introduction to the basic matrix computations, including Gaussian elimination and LU decomposition. It balances theory and algorithms and is suitable for undergraduate and graduate students. It good resource for both understanding the concepts and implementing algorithms.
This textbook provides a clear and concise introduction to linear algebra, covering Gaussian elimination as a primary method for solving linear systems. It is well-regarded for its geometric intuition and is suitable for undergraduate students. It is often used as a textbook and helps in gaining a broad understanding.
While a broader numerical analysis book, this text provides a detailed treatment of Gaussian elimination from a computational perspective, including considerations of pivoting and error analysis. It is valuable for deepening understanding, especially for those interested in the numerical aspects and is often used in undergraduate numerical methods courses.
This classic text in numerical analysis that includes a rigorous treatment of Gaussian elimination and error analysis. It is suitable for graduate students and provides a deep understanding of the theoretical underpinnings. It's a valuable reference for those pursuing advanced studies.
Provides a solid introduction to numerical analysis, covering Gaussian elimination and related topics. It is suitable for advanced undergraduate students and offers a good balance of theory and practical methods. It helps solidify understanding of the numerical aspects.
Provides a rigorous exposition of linear algebra and matrix analysis with a focus on applications in statistics. It covers Gaussian elimination and related decompositions, making it relevant for students and professionals in statistics. It good resource for understanding the role of Gaussian elimination in statistical contexts.
Takes a more abstract approach to linear algebra, focusing on vector spaces and linear operators. While it covers Gaussian elimination, it does so in the context of a broader theoretical framework. It is excellent for deepening theoretical understanding, particularly for advanced undergraduates and graduate students.
Focuses on numerical methods with implementations in MATLAB, including Gaussian elimination. It is practical-oriented and suitable for undergraduate students in science and engineering. It is useful for understanding how to apply Gaussian elimination in a computational environment.
Similar to the MATLAB-based book, this text covers numerical methods, including Gaussian elimination, using Python. It is suitable for engineering students and provides practical examples and code for implementation. It good resource for those who prefer Python.
Covers scientific computing using Python and likely includes implementations of fundamental algorithms like Gaussian elimination. It's a practical resource for those who want to apply Gaussian elimination in computational projects. It's useful for solidifying understanding through implementation.
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