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| # VIDEOS FOR CHAPTER 2 | ||
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| [Elementary Matrix Operations]([https://www.youtube.com/watch?v=27h1lN6Lx1I]) This video describes elementary matrix (row/column) operations with illustrated examples.. | ||
| [Video 1. Elementary Matrix Operations](https://www.youtube.com/watch?v=27h1lN6Lx1I) This video describes elementary matrix (row/column) operations with illustrated examples.. | ||
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| [Solution of Upper-/Lower Triangular System of Linear Equations](https://www.youtube.com/watch?v=OD53a2GlTyU) This video describes forward and backward substitution algorithms, using 4 x 4 upper- and lower-triangular system of linear equations. | ||
| [Video 2. Solution of Upper-/Lower Triangular System of Linear Equations](https://www.youtube.com/watch?v=OD53a2GlTyU) This video describes forward and backward substitution algorithms, using 4 x 4 upper- and lower-triangular system of linear equations. | ||
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| [Matrix Inversion using the Gauss-Jordan Method] (https://www.youtube.com/watch?v=3qlvkEkMKYU) This video illustrates the matrix inversion of a 4x4 matrix using the Gauss-Jordan Method. | ||
| [Video 3. Matrix Inversion using the Gauss-Jordan Method] (https://www.youtube.com/watch?v=3qlvkEkMKYU) This video illustrates the matrix inversion of a 4x4 matrix using the Gauss-Jordan Method. | ||
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| [Naive Gauss Elimination & Gauss Jordan Methods] (https://www.youtube.com/watch?v=bD7kEly3nwU) In this video lecture, the general procedure for solving systems of linear equations with naive Gauss elimination is presented. A numerical example involving a four-by-four system of linear equations is used to illustrate the Gauss Elimination and Gauss Jordan methods. | ||
| [Video 4. Naive Gauss Elimination & Gauss Jordan Methods] (https://www.youtube.com/watch?v=bD7kEly3nwU) In this video lecture, the general procedure for solving systems of linear equations with naive Gauss elimination is presented. A numerical example involving a four-by-four system of linear equations is used to illustrate the Gauss Elimination and Gauss Jordan methods. | ||
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| [Gauss Elimination with Partial Pivoting] (https://www.youtube.com/watch?v=Rbw24G9HQec) This lecture video covers the solution of system of linear equations using the direct method of Gauss Elimination with Partial Pivoting. A system of four by four equations is used to illustrate the step by step solution procedure. | ||
| [Video 5. Gauss Elimination with Partial Pivoting] (https://www.youtube.com/watch?v=Rbw24G9HQec) This lecture video covers the solution of system of linear equations using the direct method of Gauss Elimination with Partial Pivoting. A system of four by four equations is used to illustrate the step by step solution procedure. | ||
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| [Ill-Conditioned Linear Systems and Ill-Conditioned Matrices] (https://www.youtube.com/watch?v=D6Zp9XIJ8Do) Norms of the vectors and matrices are covered. Types of condition numbers and estimation tools are presented. Ill-Conditioned matrices and linear systems are illustrated with examples. | ||
| [Video 6. Ill-Conditioned Linear Systems and Ill-Conditioned Matrices] (https://www.youtube.com/watch?v=D6Zp9XIJ8Do) Norms of the vectors and matrices are covered. Types of condition numbers and estimation tools are presented. Ill-Conditioned matrices and linear systems are illustrated with examples. | ||
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| [Decomposition Methods, The Doolittle Algorithm] (https://www.youtube.com/watch?v=iZ8jWcekSPw) This video discusses Doolittle LU Decomposition algorithm with its benefits and drawbacks. The method is explained using a numerical example. | ||
| [Video 7. Decomposition Methods, The Doolittle Algorithm] (https://www.youtube.com/watch?v=iZ8jWcekSPw) This video discusses Doolittle LU Decomposition algorithm with its benefits and drawbacks. The method is explained using a numerical example. | ||
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| [Decomposition Methods, The Cholesky Decomposition] (https://www.youtube.com/watch?v=5QL1Hx5WXUQ) This video covers Cholesky Decomposition (or Cholesky Factorization) method and includes a numerical example. | ||
| [Video 8. Decomposition Methods, The Cholesky Decomposition] (https://www.youtube.com/watch?v=5QL1Hx5WXUQ) This video covers Cholesky Decomposition (or Cholesky Factorization) method and includes a numerical example. | ||
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| [Thomas Algorithm For Tridiagonal Systems and Tridiagonal Matrix Decomposition Algorithms] (https://www.youtube.com/watch?v=1HjbCWQKYjk) This video covers the Thomas Algorithm for solving a tridiagonal system of equations. A numerical example that illustrates how the Thomas algorithm works is presented. The LU decomposition of non-symmetric as well as Cholesky decomposition of tridiagonal systems are covered. | ||
| [Video 9. Thomas Algorithm For Tridiagonal Systems and Tridiagonal Matrix Decomposition Algorithms] (https://www.youtube.com/watch?v=1HjbCWQKYjk) This video covers the Thomas Algorithm for solving a tridiagonal system of equations. A numerical example that illustrates how the Thomas algorithm works is presented. The LU decomposition of non-symmetric as well as Cholesky decomposition of tridiagonal systems are covered. |