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- https://math.libretexts.org/Courses/De_Anza_College/Linear_Algebra%3A_A_First_Course/04%3A_R/4.09%3A_Gram-Schmidt_ProcessThe Gram-Schmidt process is an algorithm to transform a set of vectors into an orthonormal set spanning the same subspace, that is generating the same collection of linear combinations.
- https://math.libretexts.org/Workbench/Math_26%3A_Introduction_to_Linear_Algebra/04%3A_Vector_Spaces/4.04%3A_Stochastic_MatricesThis page explores stochastic matrices and their applications in difference equations and Markov chains, particularly in Google's PageRank algorithm. It defines difference equations, highlights the si...This page explores stochastic matrices and their applications in difference equations and Markov chains, particularly in Google's PageRank algorithm. It defines difference equations, highlights the significance of eigenvalues and long-term behavior, and discusses the Perron-Frobenius theorem.
- https://math.libretexts.org/Courses/De_Anza_College/Linear_Algebra%3A_A_First_Course/01%3A_Systems_of_Equations/1.07%3A_Gauss-Seidel_MethodWe consider an iterative method of solving a linear system in this section. Elimination methods, such as Gaussian elimination, are prone to large round-off errors for a large set of equations. Iterati...We consider an iterative method of solving a linear system in this section. Elimination methods, such as Gaussian elimination, are prone to large round-off errors for a large set of equations. Iterative methods, such as the Gauss-Seidel method, give the user control of the round-off error.
- https://math.libretexts.org/Bookshelves/Mathematical_Logic_and_Proof/Gentle_Introduction_to_the_Art_of_Mathematics_(Fields)/01%3A_Introduction_and_Notation/1.05%3A_Some_Algorithms_of_Elementary_Number_TheoryAn algorithm is simply a set of clear instructions for achieving some task. The Persian mathematician and astronomer Al-Khwarizmi1 was a scholar at the House of Wisdom in Baghdad who lived in the 8th...An algorithm is simply a set of clear instructions for achieving some task. The Persian mathematician and astronomer Al-Khwarizmi1 was a scholar at the House of Wisdom in Baghdad who lived in the 8th and 9th centuries A.D. He is remembered for his algebra treatise Hisab al-jabr w’al-muqabala from which we derive the very word “algebra,” and a text on the Hindu-Arabic numeration scheme.
- https://math.libretexts.org/Bookshelves/Linear_Algebra/Interactive_Linear_Algebra_(Margalit_and_Rabinoff)/05%3A_Eigenvalues_and_Eigenvectors/5.05%3A_Stochastic_MatricesThis page explores stochastic matrices and their applications in difference equations and Markov chains, particularly in Google's PageRank algorithm. It defines difference equations, highlights the si...This page explores stochastic matrices and their applications in difference equations and Markov chains, particularly in Google's PageRank algorithm. It defines difference equations, highlights the significance of eigenvalues and long-term behavior, and discusses the Perron-Frobenius theorem.
- https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/Discrete_Mathematics_for_Computer_Science_(Fitch)/01%3A_Basics/1.03%3A_Set_OperationsThis page offers an introduction to fundamental set operations in mathematics, including union, intersection, difference, complement, power sets, and Cartesian products, with definitions and examples....This page offers an introduction to fundamental set operations in mathematics, including union, intersection, difference, complement, power sets, and Cartesian products, with definitions and examples. It features student practice checkpoints and emphasizes the role of universal sets and algorithmic complexity in problem-solving. Overall, it serves as a beginner's guide to set theory concepts.
