Course11110710660 lectures
Numerical Linear Algebra
Prof. P.N. Agrawal Prof. D. N Pandey · IIT Roorkee
Lectures
Unit-1
- Matrix Operations and Types of Matrices
- Determinant of a Matrix
- Rank of a Matrix
- Vector Space-I
- Vector Space-II
Unit-2
- Linear dependence and independence
- Bases and Dimension - I
- Bases and Dimension - II
- Linear Transformation - I
- Linear Transformation - II
Unit-3
- Orthogonal Subspaces
- Row Space, Column Space and Null Space
- Eigen Values & Eigen Vectors-I
- Eigen Values & Eigen Vectors-II
- Diagonalizable Matrices
Unit-4
- Orthogonal Sets
- Gram Schmidt ortthogonalization and orthogonal bases
- Introduction to Matlab
- Sign Integer Representation
- Computer Representation of Numbers
Unit-5
- Floating Point Representation
- Round-off Error
- Error Propagation in Computer Arithmetic
- Addition and Multiplication of Floating Point Numbers
- Conditioning and Condition Numbers-I
Unit-6
- Conditioning and Condition Numbers-II
- Stability of Numerical Algorithms-I
- Stability of Numerical Algorithms-II
- Vector Norms - I
- Vector Norms - II
Unit-7
- Matrix Norms - I
- Matrix Norms - II
- Convergent Matrices - I
- Convergent Matrices - II
- Stability of non linear system
Unit-8
- Condition number of a matrix: Elementary Properties
- Sensitivity Analysis-I
- Sensitivity Analysis-II
- Residual Theorem
- Nearness to Singularity
Unit-9
- Estimation of the Condition Number
- Singular value decomposition of a matrix - I
- Singular value decomposition of a matrix - II
- Orthonormal Projections
- Algebraic and geometric properties of SVD
Unit-10
- SVD and their applications
- Perturbation theorem for singular values
- Outer product expansion of a matrix
- Least square solutions - I
- Least square solutions - II
Unit-11
- Householder matrices
- Householder matrices and their applications
- Householder QR factorization- I
- Householder QR factorization- II
- Basic theorems on eigenvalues and QR method
Unit-12
Syllabus and materials
At NPTEL, as the course publishes them.
Credits and licence
- Institution
- IIT Roorkee
- Department
- Mathematics
- Teacher
- Prof. P.N. Agrawal Prof. D. N Pandey
- Level
- Undergraduate
- Language
- English
- Subjects
- Mathematics
- Source
- NPTEL
- Licence
- CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
- Attribution
- NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
- Who can watch
- NPTEL gives no rating. Invisible Network shows it to Tweens profiles and older, judged from what the source says about it. How courses are placed
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