Lecture Notes 24

Lecture Notes 24 - Lecture24 q Lecture 24: The End....

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q Outline: 1) Course Review: putting it all together 2) The Future: two great directions A) Linear PDE's: from the discrete to the continuous (finite dimensional to infinite dimensional vector spaces) from the continuous to the discrete Lecture 24: The End. .. Course Overview: the big picture: short form subject: Equations: Algorithms: Factorizations: Theory: Applications: Linear Systems Eigen Problems Least Squares Ax =b Ax = λ x A T Ax =A T b Elimination (Gauss,GJordan) Gram-Schmidt factor P( λ )=|A- λ I| Find N(A- λ i I) PA=LU PA=LDL T A=CC T A = QR AS = S Λ A = S Λ S -1 A = Q Λ Q T A = U Σ V T Invertibility and A -1 Vector Spaces/Subspaces 4 Subspaces of A General solutions to Ax =b Orthogonality Projections Projection Matrices Q Matrices Eigenvalues/Eigenvec The Determinant Diagonalization Symmetric Matrices The SVD Solving Linear systems e.g. Spring Block Least Squares fitting of functions Finding Projections Matrix Powers A
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This note was uploaded on 06/02/2010 for the course APMA APMA E3101 taught by Professor Spiegelman during the Fall '07 term at Columbia.

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Lecture Notes 24 - Lecture24 q Lecture 24: The End....

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