C S C I 2 0 3 3
Lecture Notes
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- Set number 16 : Full size:
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Posted on:
Mon Apr 23 06:59:21 CDT 2018
Topics:
Eigenvalues end eigenvectors; Diagonalization;
The Singular value decomposition; Applications.
- Set number 15 : Full size:
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Posted on:
Mon Apr 16 07:55:03 CDT 2018
Reposted Thu Apr 26 14:37:45 CDT 2018
Pages 15-14 to 15-15 added.
Topics:
Orthogonality and least-squares - continued;
Orthogonal systems of vectors; The Gram-Schmidt algorithm;
The QR factoriozation. Least-squares via QR
- Set number 14 : Full size:
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Posted on:
Thu Apr 5 18:18:27 CDT 2018. Reposted Fri Apr 6 07:16:52 CDT 2018.
Topics:
Orthogonality and least-squares problems;
Inner products and norms; Basic inequalities;
Orthogonal spaces; Least-squares problems; Applications.
- Set number 13 : Full size:
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Tue Apr 3 15:11:55 CDT 2018
Topics:
Application: mappings. Representing rotations, translations
Combining rotations and translations, Homogenous coordinates
- Set number 12 : Full size:
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Posted on:
Fri Mar 30 09:31:24 CDT 2018
Topics:
Linear independence revisited; Bases; Standard bases;
Bases for the null space and for the column space;
Dimension of a subspace; Rank of a matrix.
- Set number 11 : Full size:
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Thu Mar 22 15:10:09 CDT 2018
Topics:
General vector spaces; Examples; Subspaces;
The Null and the Column space of a matrix.
- Set number 10 : Full size:
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Thu Mar 8 09:04:44 CST 2018
Topics:
Determinants. Properties of 2x2 determinants;
General definition of nxn determinants; cofactors;
Applications: matrix inversion, areas in 2-dimens. spaces;
Volumes in 3-dimens. spaces.
- Set number 9 : Full size:
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Posted on:
Mon Feb 26 18:17:49 CST 2018
Topics:
The LU factorization; Motivation; Elimination matrices;
How to compute L; Applications of the LU factorization.
- Set number 8 : Full size:
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Posted on:
Sun Feb 18 16:17:08 CST 2018
Re-posted
Fri Mar 2 11:29:03 CST 2018
with changes and additions at end
Topics:
The inverse of a matrix; Point of view of mappings;
Properties; General results on existence of the inverse;
Elementary matrices and the inverse; Computing the inverse
- Set number 7 : Full size:
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Posted on:
Mon Feb 12 17:42:51 CST 2018;
Re-posted Wed Feb 21 08:06:56 CST 2018
with additions (3 pages after p. 7-8)
Topics:
Linear Mappings; Linear vs. nonlinear mappings;
Matrices as mappings; Matrices; Matrix operations;
Transposition; Addition or matrices; Product of matrices.
- Set number 6 : Full size:
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Tue Feb 6 17:47:23 CST 2018 and Re-posted on:
Fri Feb 9 17:58:14 CST 2018 with additions at end.
Topics:
The matrix equation Ax=b. Matrix-vector products;
Existence of solutions. Application: Markov chain models.
Application: Economic models; Google PageRank.
- Set number 5 : Full size:
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Posted on:
Wed Jan 31 09:03:55 CST 2018
Topics:
Vectors and the space R^n; operations with vectors;
Linear combinations of vectors;
The span of a set of vectors;
Geometric representations;
Linear Independence of vectors;
Determining linear independence.
- Set number 4 : Full size:
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Posted on:
Wed Jan 24 08:43:25 CST 2018
Topics:
Matlab: explanation of gauss.m script;
The row echelon form; reduced row echelon form;
Computing the standard and reduced row echelon form;
Applications; General solution of a linear system.
- Set number 3 : Full size:
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Posted on:
Sun Jan 21 09:48:43 CST 2018
Topics:
Sec. [1.1] from text; Solving Systems of equations;
Augmented form; Equivalent systems; Row operations;
Gaussian elimination; Pivoting; Gauss-Jordan Elimination.
- Set number 2 : Full size:
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Posted on:
Wed Jan 17 18:17:52 CST 2018
Topics:
A brief introduction to Matlab; Getting help;
Simple matlab commands; If statements; Loops;
Array constructs; Simple plotting.
- Set number 1 : Full size:
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Posted on:
Tue Jan 16 13:00:38 CST 2018
Topics:
Background algorithms; Complexity; Linear Systems;
Solving triangular systems.