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Triangular decomposition

In computer algebra, a triangular decomposition of a polynomial system S is a set of simpler polynomial systems S1, ..., Se such that a point is a solution of S if and only if it is a solution of one of the systems S1, ..., Se. When the purpose is to describe the solution set of S in the algebraic closure of its coefficient field, those simpler systems are regular chains. If the coefficients of the polynomial systems S1, ..., Se are real numbers, then the real solutions of S can be obtained by a triangular decomposition into regular semi-algebraic systems. In both cases, each of these simpler systems has a triangular shape and remarkable properties, which justifies the terminology. (Wikipedia).

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LU decomposition of matrices

In LU decomposition we decompose a matrix into two matrices, that, when multiplied in a certain order, gives rise to the original matrix. L is a lower triangular matrix, and U is an upper triangular matrix. An upper triangular matrix has entries equaling zero below the main diagonal and a

From playlist Introducing linear algebra

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LU Decomposition - Shortcut Method

This video explains how to find the LU Decomposition of a square matrix using a shortcut involving the opposite of multipliers used when performing row operations. Site: http://mathispower4u.com Blog: http://mathispower4u.wordpress.com

From playlist Matrix Equations

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LU Decomposition Using Elementary Matrices

This video explains how find the LU Decomposition of a square matrix using elementary matrices. Site: http://mathispower4u.com Blog: http://mathispower4u.wordpress.com

From playlist Matrix Equations

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QR decomposition

QR Decomposition of a matrix and applications to least squares Check out my Orthogonality playlist: https://www.youtube.com/watch?v=Z8ceNvUgI4Q&list=PLJb1qAQIrmmAreTtzhE6MuJhAhwYYo_a9 Subscribe to my channel: https://www.youtube.com/channel/UCoOjTxz-u5zU0W38zMkQIFw

From playlist Orthogonality

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Learn how to determine the surface area of a triangular pyramid

👉 Learn how to find the volume and the surface area of a pyramid. A pyramid is a 3-dimensional object having a polygon as its base and triangular surfaces converging at a single point called its apex. A pyramid derives its name from the shape of its base, i.e. a pyramid with a triangular b

From playlist Volume and Surface Area

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Solve a System of Linear Equations Using LU Decomposition

This video explains how to use LU Decomposition to solve a system of linear equations. Site: http://mathispower4u.com Blog: http://mathispower4u.wordpress.com

From playlist Matrix Equations

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Reduction to Triangular Form

A technique for finding determinants using row operations to obtain a triangular matrix. This video screencast was created with Doceri on an iPad. Doceri is free in the iTunes app store. Learn more at http://www.doceri.com

From playlist Linear Algebra

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Review of Decomposition by the Dot Product

https://bit.ly/PavelPatreon https://lem.ma/LA - Linear Algebra on Lemma http://bit.ly/ITCYTNew - Dr. Grinfeld's Tensor Calculus textbook https://lem.ma/prep - Complete SAT Math Prep

From playlist Part 4 Linear Algebra: Inner Products

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Mod-01 Lec-18 L U decomposition

Elementary Numerical Analysis by Prof. Rekha P. Kulkarni,Department of Mathematics,IIT Bombay.For more details on NPTEL visit http://nptel.ac.in

From playlist NPTEL: Elementary Numerical Analysis | CosmoLearning Mathematics

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Linear Algebra 13e: The LU Decomposition

https://bit.ly/PavelPatreon https://lem.ma/LA - Linear Algebra on Lemma http://bit.ly/ITCYTNew - Dr. Grinfeld's Tensor Calculus textbook https://lem.ma/prep - Complete SAT Math Prep

From playlist Part 1 Linear Algebra: An In-Depth Introduction with a Focus on Applications

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Mod-01 Lec-39 Q R Decomposition

Elementary Numerical Analysis by Prof. Rekha P. Kulkarni,Department of Mathematics,IIT Bombay.For more details on NPTEL visit http://nptel.ac.in

From playlist NPTEL: Elementary Numerical Analysis | CosmoLearning Mathematics

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Mod-01 Lec-19 Cholesky decomposition

Elementary Numerical Analysis by Prof. Rekha P. Kulkarni,Department of Mathematics,IIT Bombay.For more details on NPTEL visit http://nptel.ac.in

From playlist NPTEL: Elementary Numerical Analysis | CosmoLearning Mathematics

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Learn how to determine the surface area of a triangular prism

👉 Learn how to find the volume and the surface area of a pyramid. A pyramid is a 3-dimensional object having a polygon as its base and triangular surfaces converging at a single point called its apex. A pyramid derives its name from the shape of its base, i.e. a pyramid with a triangular b

From playlist Volume and Surface Area

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Mod-01 Lec-24 Tutorial 3

Elementary Numerical Analysis by Prof. Rekha P. Kulkarni,Department of Mathematics,IIT Bombay.For more details on NPTEL visit http://nptel.ac.in

From playlist NPTEL: Elementary Numerical Analysis | CosmoLearning Mathematics

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Linear Algebra 9.1 LU-Decompositions

My notes are available at http://asherbroberts.com/ (so you can write along with me). Elementary Linear Algebra: Applications Version 12th Edition by Howard Anton, Chris Rorres, and Anton Kaul A. Roberts is supported in part by the grants NSF CAREER 1653602 and NSF DMS 2153803.

From playlist Linear Algebra

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Determining the volume of rectangular pyramid

👉 Learn how to find the volume and the surface area of a pyramid. A pyramid is a 3-dimensional object having a polygon as its base and triangular surfaces converging at a single point called its apex. A pyramid derives its name from the shape of its base, i.e. a pyramid with a triangular b

From playlist Volume and Surface Area

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LU Decomposition with Partial Pivoting | Lecture 26 | Numerical Methods for Engineers

How to do LU decomposition of a matrix using partial pivoting. Join me on Coursera: https://www.coursera.org/learn/numerical-methods-engineers Lecture notes at http://www.math.ust.hk/~machas/numerical-methods-for-engineers.pdf Subscribe to my channel: http://www.youtube.com/user/jchasno

From playlist Numerical Methods for Engineers

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Real closed field | Axiom (computer algebra system) | Algebraically closed field | Maple (software) | Regular semi-algebraic system | Computer algebra | Algebraic closure | Regular chain | Field (mathematics) | Wu Wenjun | Generic point | Polynomial ring | Wu's method of characteristic set | Algebraic variety